Question 13 Marks
Solve the following equation by trial and error method:
$2x - 3 = 9$
AnswerThe given equation is $2x - 3 = 9$
We guess and try several values of $x$ to find $L.H.S.$ and $R.H.S.$ and stop when $L.H.S. = R.H.S.$
|
x
|
L.H.S.
|
R.H.S.
|
|
$3$
|
$2 \times 3 - 3 = 3$
|
$9$
|
|
$4$
|
$2 \times 4 - 3 = 5$
|
$9$
|
|
$5$
|
$2 \times 5 - 3 = 7$
|
$9$
|
|
$6$
|
$2 \times 6 - 3 = 9$
|
$9$
|
When $x = 6$, we have $L.H.S. = R.H.S$
So, $x = 6$ is the solution of the given equation. View full question & answer→Question 23 Marks
Solve: $\frac{\text{2x}}{5}-\frac{\text{x}}{2}=\frac{5}{2}$
Answer$\frac{\text{2x}}{5}-\frac{\text{x}}{2}=\frac{5}{2}$ Or,
$\frac{\text{4x-5x}}{10}=\frac{5}{2}$ [Taking $L.C.M.$ as $10]$
$\Rightarrow\frac{\text{x}}{10}=\frac{5}{2}$
$\Rightarrow\frac{\text{x}}{10}\times(-10)=\frac{5}{2}\times(-10)$ [Multiplying both the sides by $(-10)] \text{x}=-25$
View full question & answer→Question 33 Marks
Solve the following equation and verify the answer: $x - 7 = 6$
Answer$x - 7 = 6$ Adding $7$ on both the sides:
$\Rightarrow x - 7 + 7 = 6 + 7 $
$\Rightarrow x = 13$
Verification: Substituting $x = 13$ in the $L.H.S. $
$\Rightarrow 13 - 7 = 6 = R.H.S. $
$L.H.S. = R.H.S$. Hence, verified.
View full question & answer→Question 43 Marks
When Raju multiplies a certain number by $17$ and adds $4$ to the product, he gets $225$. Find that number.
AnswerLet the required number is $x$Then, $17x + 4 = 225$
Or, $17x = 225 - 4$
$\Rightarrow\text{x}=\frac{221}{17}$
$x = 13$
So, the number is $13$
View full question & answer→Question 53 Marks
Solve the following equation and verify the answer: $x + 5 = 12$
Answer$x + 5 = 12$
Subtracting $5$ from both the sides:
$\Rightarrow x + 5 - 5 = 12 - 5 $
$\Rightarrow x = 7$
Verification: Substituting $x = 7$ in the $L.H.S. $
$\Rightarrow 7 + 5 = 12 = R.H.S. $
$L.H.S. = R.H.S.$
Hence, verified.
View full question & answer→Question 63 Marks
If a number is tripled and the result is increased by $5$, we get $50$. Find the number.
AnswerLet the required numbers is $x$
Then, $3x + 5 = 50$
Or, $3x = 50 - 5$
$\Rightarrow\text{x}=\frac{45}{3}$
$x = 15$
So, the number is $15$
View full question & answer→Question 73 Marks
Solve the following equation and verify the answer: $4x + 7 = 15$
Answer$4x + 7 = 15 $
$\Rightarrow 4x + 7 - 7 = 15 - 7$ [Subtracting $7$ from both the sides]
$\Rightarrow 4x = 8$
$\Rightarrow\frac{\text{4x}}{4}=\frac{8}{4}$ [Dividing both the sides by $4]$
$\Rightarrow x = 2$
Verification: Substituting $x = 2$ in the $L.H.S. $
$\Rightarrow 4 \times 2 + 7 = 8 + 7 = 15 = R.H.S.$
$ L.H.S. = R.H.S.$
Hence, verified.
View full question & answer→Question 83 Marks
Solve the following equation by trial and error method: $x - 7 = 10$
AnswerThe given equation is $x - 1 = 10$ We guess and try several values of $x$ to find $L.H.S.$ and $R.H.S.$ and stop when $L.H.S. = R.H.S.$
| x |
L.H.S. |
R.H.S. |
| $14$ |
$14 - 7 = 7$ |
$10$ |
| $15$ |
$15 - 7 = 8$ |
$10$ |
| $16$ |
$16 - 7 = 9$ |
$10$ |
| $17$ |
$17 - 7 = 10$ |
$10$ |
When $x = 17$,
we have $L.H.S. = R.H.S$
So $x = 17$ is the solution of the given equation. View full question & answer→Question 93 Marks
The length of a rectangular park is thrice its breadth. If the perimeter of the park is $168$ metres, fund its dimensions.
AnswerLet the Breadth of the park is $x m$. and length is $3x m.$
Then, $2(x + 3x) = 168$ Or, $2x + 6x = 168 $
$\Rightarrow 8x = 168$
$\Rightarrow\text{x}=\frac{168}{8}$
$x = 21$
So, the breadth is $21m$ and length is $(3 \times 21) = 63m$
View full question & answer→Question 103 Marks
The sum of three consecutive natural numbers is $51$. Find the numbers.
AnswerLet the three consecutive natural numbers be $x, (x + 1)$ and $(x + 2)$
$\therefore x + (x + 1) + (x + 2) = 51$
$\Rightarrow 3x + 3 = 51 $
$\Rightarrow 3x + 3 - 3 = 51 - 3$ [Subtracting $3$ from both the sides]
$\Rightarrow 3x = 48$
$\Rightarrow\frac{\text{3x}}{3}=\frac{48}{3}$
[Dividing both the sides by $3] x = 16$
Thus, the three natural numbers are $x = 16, x + 1 = 17$ and $x + 2 = 18$
View full question & answer→Question 113 Marks
A man is thrice as old as his son. Five years ago the man was four times as old as his son. Find their present ages.
AnswerLet the age of son is $x$ and and age of the man is $3x$ Before $5$ years their age are $(x - 5)$ and $(3x - 5)$
Then, $3x - 5 = 4(x - 5)$ Or, $3x - 5 = 4x - 20 $
$\Rightarrow 3x - 4x = -20 + 5 $
$\Rightarrow -x = -15 x = 15$
So, present age of the son is $15$ years and present age of the man is $(3 \times 15) = 45$ years
View full question & answer→Question 123 Marks
The number of boys in a school is $334$ more than the number of girls. If the total strength of the school is $572$, find the number of girls in the school.
AnswerLet the number of girls is $x$
Then, $x + 334 + x = 572$ Or, $2x = 572 - 334$
$\Rightarrow\text{x}=\frac{238}{2} x = 119$
So, the number of girls is $119$
View full question & answer→Question 133 Marks
Lalit earns $Rs. x$ per day and spends $Rs. y$ per day. How much does he save in $30$ days?
AnswerLalit's earning per day $= Rs. x$
$\therefore$ Lalit's earning in $30$ days $= Rs. 30 \times x = Rs. 30x$
Similarly, Lalit's expenditure per day $= Rs. y$
$\therefore$ Lalit's expenditure in $30$ days $= Rs. 30 \times y = Rs. 30 y$
$\therefore$ In $30$ days, Lalit saves = (Total earnings - Total expenditure) $= Rs. (30x - 30y) = Rs. 30(x - y)$
View full question & answer→Question 143 Marks
Solve the following equation and verify the answer: $3(x + 6) = 24$
Answer$3(x + 6) = 24$
$\Rightarrow\frac{3(\text{x}+6)}{3}=\frac{24}{3}$ (Dividing both sides by $3)$
$x + 6 = 8 $
$\Rightarrow x = 8 - 6$ (Transposing $6$ to $R.H.S.) $
$\Rightarrow x = 2 x = 2$ is a solution of the given equation.
Check: Substituting the value of $x = 2$ in the given equation,
we get $L.H.S. = 3(2 + 6 ) = 3 \times 8 = 24$ and $RH.S. = 24$
$\therefore$ When $x = 2$, we have $L.H.S. = R.H.S.$
View full question & answer→Question 153 Marks
Solve the following equation by trial and error method: $2y + 4 = 3y$
View full question & answer→Question 163 Marks
Solve the following equation by trial and error method: $y + 9 = 13$
AnswerThe given equation is $y + 9 = 13$ We try several values of $y$ and find $L.H.S$. and the $R.H.S$. and stop when $L.H.S. = R.H.S.$
| y |
L.H.S. |
R.H.S. |
| $2$ |
$2 + 9 = 11$ |
$13$ |
| $3$ |
$3 + 9 = 12$ |
$13$ |
| $4$ |
$4 + 9 = 13$ |
$13$ |
When $y = 4$, we have $L.H.S. = R.H.S.$ So $y = 4$ is the solution of the given equation. View full question & answer→Question 173 Marks
The length of a rectangular hall is $5$ metres more than its breadth. If the perimeter of the hall is $74$ metres, find its length and breadth.
AnswerLet the breadth of the hall is $x m$. and length is $(x + 5)$ m.
Then, $2(x + x + 5) = 74$ Or, $4x + 10 = 74$
$\Rightarrow 4x = 74 - 10$
$\Rightarrow\text{x}=\frac{64}{4}$
$x = 16$
So, the breadth is 16m and the length is $(16 + 5) = 21m$
View full question & answer→Question 183 Marks
After $32$ years, Rahim will be $5$ times as old as he was $8$ years ago. How old is Rahim today?
AnswerLet the age of Rahim be $x$ years After $32$ years his age is $x + 32$ years.
$8$ years ago his age was $(x - 8)$
Then, $5(x - 8) = x + 32$ Or, $5x - 40 = x + 32 $
$\Rightarrow 5x - x = 32 + 40 $
$\Rightarrow 4x = 72$
$\Rightarrow\text{x}=\frac{72}{4}$
$x = 18$
So, Rahim is $18$ years old today
View full question & answer→Question 193 Marks
Solve the following equation by trial and error method:
$11 + x = 19$
AnswerThe given equation is $11 + x = 19$
We try several values of $x$ and find $L.H.S.$ and the $R.H.S.$ and stop when $L.H.S. = R.H.S$.
| x |
L.H.S. |
R.H.S. |
| $3$ |
$11 + 3 = 14$ |
$19$ |
| $4$ |
$11 + 4 = 15$ |
$19$ |
| $6$ |
$11 + 6 = 17$ |
$19$ |
| $7$ |
$11 + 7 = 18$ |
$19$ |
| $8$ |
$11 + 8 = 9$ |
$19$ |
When $x = 8$, we have $L.H.S. = R.H.S.$
So $x = 8$ is the solution of the given equation. View full question & answer→Question 203 Marks
The cost of $1$ pen is $Rs. 16$ and the cost of $1$ pencil is $Rs. 5$. What is the total cost of $x$ pens and $y$ pencils.
AnswerCost of $1$ pen $= Rs. 16$
$\therefore$ Cost of $x$ pens $= Rs. 16 × x = Rs. 16x $Similarly, cost of $1$ pencil $= Rs. 5$
$\therefore$ Cost of $y$ pencils $= Rs. 5 × y = Rs. 5y$
$\therefore$ Total cost of $x$ pens and $y$ pencils $= Rs. (16x + 5y)$
View full question & answer→Question 213 Marks
Three times a number added to $8$ gives $20$. Find the number.
AnswerLet the required number be x Three times this number is $3x$ On adding $8,$
the number becomes $3x + 8 3x + 8 = 20$ Or, $3x + 8 - 8 = 20 - 8$ [Subtracting $8$ from both the sides]
$\Rightarrow 3x = 12$
$\Rightarrow\frac{\text{3x}}{3}=\frac{12}{3}$ [Dividing both the sides by $3] $
$\Rightarrow x = 4$
$\therefore$ Required number $= 4$
View full question & answer→Question 223 Marks
Solve the following equation by trial and error method: $z - 3 = 2z - 5$
AnswerThe given equation is $z - 3 = 2z - 5$ We guess and try several values of z to find $L.H.S.$ and $R.H.S.$ and stop when $L.H.S. = R.H.S.$
|
x
|
L.H.S.
|
R.H.S.
|
|
$1$
|
$1 - 3 = -2$
|
$2 \times 1 - 5 = -3$
|
|
$2$
|
$2 - 3 = -1$
|
$2 \times 2 - 5 = -1$
|
When $z = 2$, we have $L.H.S. = R.H.S$ So, $z = 2$ is the solution of the given equation. View full question & answer→Question 233 Marks
After $16$ years, Fatima will be three times as old as she is now. Find her present age.
AnswerThen, $3x = x + 16$
Or, $3x - x = 16$
$\Rightarrow 2x = 16$
$\Rightarrow\text{x}=\frac{16}{2}$
$\Rightarrow x = 8$
So, the present age of fatima is $8$ years
View full question & answer→Question 243 Marks
Solve the following equation and verify the answer: $x - 2 = -5$
Answer$x - 2 = -5$ Adding $2$ on both the sides:
$\Rightarrow x - 2 + 2 = -5 + 2 $
$\Rightarrow x = -3$
Verification: Substituting $x = -3$ in the $L.H.S. $
$\Rightarrow -3 - 2 = -5 = R.H.S. $
$L.H.S. = R.H.S.$
Hence, verified.
View full question & answer→Question 253 Marks
Solve the following equation and verify the answer: $\frac{\text{x}}{5}=12$
Answer$\frac{\text{x}}{5}=12$
$\Rightarrow\frac{\text{x}}{5}\times5=12\times5$ [Multiplying both the sides by $5]$
$\Rightarrow \text{x}=60$
Verification: Substituting $x = 60$ in the $L.H.S.$
$\Rightarrow\frac{60}{5}=12=\text{R.H.S.}$
$\Rightarrow\text{L.H.S.}=\text{R.H.S.}$
Hence, verified.
View full question & answer→Question 263 Marks
A man is 4 times as old as his son. After $16$ years he will be only twice as old as his son. Find their present ages.
AnswerLet the age of son is $x$ and his father's age is $4x$ After $16$ years
the age of son is $x + 16$ and his father age is $4x + 16$
Then, $4x + 16 = 2(x + 16)$ Or, $4x + 16 = 2x + 32$
$\Rightarrow 4x - 2x = 32 - 16$
$\Rightarrow 2x = 16$
$\Rightarrow\text{x}=\frac{16}{2}$
$x = 8$
So, the present age of son is $8$ years and his father's age is $(4 \times 8) = 32$ years
View full question & answer→Question 273 Marks
A bag contains $25-$paisa and $50-$paisa coins whose total value is $Rs. 30$. If the number of $25-$paisa coins is four times that of $50-$paisa coins, find the number of each type of coins.
AnswerLet the amount of $50$ paise is $x$ and $25$ paise is $4 x50x + (25 \times 4x) = 50x + 100x = 150x$
And, $Rs. 30 = 3000$ paise
Then, $150x = 3000$
Or, $\text{x}=\frac{3000}{150}$
$x = 20$
So, the required number of $50$ paise is $20$ and $25$ paise is $(4 \times 20) = 80$
View full question & answer→Question 283 Marks
Solve the following equation by trial and error method: $\frac{1}{2}\text{x}+7=11$
AnswerThe given equation is $\frac{1}{2}\text{x}+7=11$ We guess and try several values of $x$ to find $L.H.S$. and $R.H.S.$ and stop when $L.H.S. = R.H.S.$
| x |
L.H.S. |
R.H.S. |
| $2$ |
$\frac{1}{2}\times2+7=8$ |
$11$ |
| $4$ |
$\frac{1}{2}\times4+7=9$ |
$11$ |
| $6$ |
$\frac{1}{2}\times6+7=10$ |
$11$ |
| $8$ |
$\frac{1}{2}\times8+7=$11$$ |
$11$ |
When $x = 8$, we have $L.H.S. = R.H.S$
So, $x = 8$ is the solution of the given equation. View full question & answer→Question 293 Marks
Solve the following equation and verify the answer: $x + 3 = -2$
Answer$x + 3 = -2$ Subtracting $3$ from both the sides:
$\Rightarrow x + 3 - 3 = -2 - 3 $
$\Rightarrow x = -5$
Verification: Substituting $x = -5$ in the $L.H.S. $
$\Rightarrow -5 + 3 = -2 = R.H.S. $
$L.H.S. = R.H.S$. Hence, verified.
View full question & answer→Question 303 Marks
Solve: $3(x + 2) - 2(x - 1) = 7$
Answer$3(x + 2) - 2(x - 1) = 7$. Or,
$3 \times x + 3 \times 2 - 2 \times x - 2 \times (-1) = 7$ [On expanding the brackets]
$\Rightarrow 3x + 6 - 2x + 2 = 7 $
$\Rightarrow x + 8 = 7 $
$\Rightarrow x + 8 - 8 = 7 - 8$ [Subtracting $8$ from both the sides]
$\Rightarrow x = −1$
View full question & answer→Question 313 Marks
Solve the following equation and verify the answer:
$6x + 5 = 2x + 17$
Answer$6x + 5 = 2x + 17 $
$\Rightarrow 6x - 2x = 17 - 5$ (Transposing $2x$ to $L.H.S$. and $5$ to $R.H.S.) $
$\Rightarrow 4x = 12$
$\Rightarrow\frac{\text{4x}}{4}=\frac{12}{4}$
(Dividing both sides by $4) $
$\Rightarrow x = 3 x = 3$ is a solution of the given equation.
Check : Substituting $x = 3$ in the given equation,
we get $L.H.S. = 6 \times 3 + 5 = 18 + 5 = 23$
$R.H.S. = 2 \times 3 + 17 = 6 + 17 = 23$
$\therefore$ When $x = 3$,
we have $L.H.S. = R.H.S.$
View full question & answer→Question 323 Marks
The sum of two consecutive even numbers is $74$. Find the numbers.
AnswerLet the required numbers are $x$ and $x + 2$
Then, $x + x + 2 = 74$ Or, $2x = 74 - 2$
$\Rightarrow\text{x}=\frac{72}{2}$
$x = 36$
So, the numbers are $36$ and $(36 + 2) = 38$
View full question & answer→Question 333 Marks
Solve the following equation and verify the answer: $3x - 5 = 13$
Answer$3x - 5 = 13$
$\Rightarrow 3x - 5 + 5 = 13 + 5$ [Adding $5$ on both the sides]
$\Rightarrow 3x = 18$
$\Rightarrow\frac{\text{3x}}{3}=\frac{18}{3}$ [Dividing both the sides by $3]$
$\Rightarrow x = 6$
Verification:
Substituting $x = 6$ in the $L.H.S.$
$\Rightarrow 3 \times 6 - 5 = 18 - 5 = 13 = R.H.S.$
$L.H.S. = R.H.S.$
Hence, verified.
View full question & answer→Question 343 Marks
If $x = 1, y = 2$ and $z = 3$, find the value of $x^2+ y^2 + 2xyz.$
AnswerGiven:
$x =1$
$y = 2$
$z = 3$
Substituting $x = 1, y = 2$ and $z = 3$ in the given equation:
$(x^2+ y^2+ 2xyz)$
$⇒ (1)^2+ ( 2)^2+ 2(1)(2)(3)$
$⇒ 1 + 4 + 12 = 17$
View full question & answer→Question 353 Marks
One out of two numbers is thrice the other. If their sum is $124$, find the numbers.
AnswerLet the required number are $x$ and $3x$
Then, $x + 3x = 124$
Or, $4x = 124$
$\Rightarrow\text{x}=\frac{124}{4}$
$x = 31$
So, the numbers are $31$ and $(3 \times 31) = 93$
View full question & answer→Question 363 Marks
Solve: $4x + 9 = 17$
Answer$4x + 9 = 17$ Or, $4x + 9 - 9 = 17 - 9$ [Subtracting $9$ from both the sides]
$\Rightarrow 4x = 8$
$\Rightarrow\frac{\text{4x}}{4}=\frac{8}{4}$ [Dividing both the sides with $4] x = 2$
View full question & answer→Question 373 Marks
Solve the following equation by trial and error method: $3y = 36$
AnswerThe given equation is $3y = 36$ We guess and try several values of $y$ to find $L.H.S.$ and $R.H.S.$ and stop when $L.H.S. = R.H.S.$
| y |
L.H.S. |
R.H.S. |
| $7$ |
$3 \times 7 = 21$ |
$36$ |
| $9$ |
$3 \times 9 = 27$ |
$36$ |
| $10$ |
$3 \times 10 = 30$ |
$36$ |
| $12$ |
$3 \times 12 = 36$ |
$36$ |
When $y = 12,$ we have $L.H.S. = R.H.S$ So $y = 12$ is the solution of the given equation. View full question & answer→Question 383 Marks
After $16$ years, Seema will be three times as old as she is now. Find her present age.
AnswerLet the present age of Seema be $x$ years. After $16$ years:
Seema's age $= x + 16$ After $16$ years, her age becomes thrice of her age now
$\therefore x + 16 = 3x$ Or, $16 = 3x - x$ [Transposing $x$ to the $R.H.S.]$
$\Rightarrow 2x = 16$
$\Rightarrow\frac{\text{2x}}{2}=\frac{16}{2}$ [Dividing both the sides by $2]$
$x = 8$ years
View full question & answer→Question 393 Marks
Find two numbers such that one of them is five times the other and their difference is $132.$
AnswerLet the required numbers are $x$ and $5x$ Then, $5x - x - = 132$ Or, $4x = 132$
$\Rightarrow\text{x}=\frac{132}{4} x = 33$
So, the numbers are $33$ and $(33 \times 5) = 165$
View full question & answer→Question 403 Marks
Five times the price of a pen is $Rs. 17$ more than three times its price. Find the price of the pen.
AnswerLet the price of each pen is xThen, $5x = 3x + 17$
Or, $5x - 3x = 17$
$\Rightarrow 2x = 17$
$\Rightarrow\text{x}=\frac{17}{2}$
$x = 8.50$
So, the price of the pen is $8.50$ rupees
View full question & answer→Question 413 Marks
Find two numbers such that one of them exceeds the other by $18$ and their sum is $92.$
AnswerLet the required number are $x$ and $x + 18$
Then, $x + x + 18 = 92$
Or, $2x = 92 - 18$
$\Rightarrow\text{x}=\frac{74}{2}$
$x = 37$
So, the numbers are $37$ and $(37 + 18) = 55$
View full question & answer→Question 423 Marks
Solve the following equation and verify the answer: $\frac{\text{3x}}{5}=15$
Answer$\frac{\text{3x}}{5}=15$ $\Rightarrow\frac{\text{3x}}{5}\times5=15\times5$ [Multiplying both the sides by 5] $\Rightarrow \text{3x}=75$ $\Rightarrow\frac{\text{3x}}{3}=\frac{75}{3}$ [Dividing both sides by 3] $\Rightarrow\text{x}=25$ Verification: Substituting x = 25 in the L.H.S.$\Rightarrow\frac{3\times25}{3}=15=\text{R.H.S.}$
$\Rightarrow\text{L.H.S.}=\text{R.H.S.}$
Hence, verified.
View full question & answer→Question 433 Marks
Mrs. Goel is $27$ years older than her daughter Rekha. After $8$ years she will be twice as old as Rekha. Find their present ages.
AnswerLet Rekha's age is $x$ years and Mrs.
Goel's age is $x + 27$ years after $8$ years the age of Rekha is $x + 8$ and Mrs.
Goel is $x + 27 + 8$
Then, $x + 27 + 8 = 2(x + 8)$ Or, $x + 35 = 2x + 16$
$⇒ 2x - x = 35 - 16$
$ x = 19$
So, the age of Rekha is 19 years and Mrs. Goel is $19 + 27 = 46$
View full question & answer→Question 443 Marks
Solve the following equation and verify the answer: $\frac{\text{x}}{4}-8=1$
Answer$\frac{\text{x}}{4}-8=1$
$\Rightarrow\frac{\text{x}}{4}=1+8$ (Transporting $-8$ to $R.H.S.)$
$\Rightarrow\frac{\text{x}}{4}=9$
$\Rightarrow\frac{\text{x}}{4}\times4=9\times4$ (Multiplying both sides by $4)$
$\Rightarrow x = 36$
$\therefore \text{x}=36$ is a solution of the given equation.
Substituting $x = 36$ in the given equation,
we get $\text{L.H.S.}=\frac{36}{4}-8=9-8=1$ and $\text{R.H.S.}=1$
$\therefore$ When $x = 36$,
we have $L.H.S. = R.H.S.$
View full question & answer→Question 453 Marks
Solve the following equation by trial and error method: $4x = 28$
AnswerThe given equation is $4x = 28$ We guess and try several values of $x$ to find $L.H.S.$ and $R.H.S.$ and stop when $L.H.S. = R.H.S.$
| x |
L.H.S. |
R.H.S. |
| $2$ |
$4 \times 2 = 8$ |
$28$ |
| $4$ |
$4 \times 4 = 16$ |
$28$ |
| $5$ |
$4 \times 5 = 20$ |
$28$ |
| $6$ |
$4 \times 6 = 24$ |
$28$ |
| $7$ |
$4 \times 7 = 28$ |
$28$ |
When $x = 7,$
we have $L.H.S. = R.H.S$
So $x = 7$ is the solution of the given equation. View full question & answer→Question 463 Marks
Solve the following equation and verify the answer: $5x - 3 = x + 17$
Answer$5x - 3 = x + 17$
$\Rightarrow 5x - x = 17 + 3$ [Transporting $x$ to $L.H.S. -3$ to $R.H.S.]$
$\Rightarrow4\text{x}=20$
$\Rightarrow\frac{\text{4x}}{4}=\frac{20}{4}$ (Dividing both sides by $4)$
$\Rightarrow x = 5$
So. $x = 5$ is a solution of the given equation.
Check: Substituting $x = 5$ in the given equation,
we get $L.H.S. = 5 \times 5 - 3 = 25 - 3 = 22 $
$R.H.S. 5 + 17 = 22$
$\therefore$ When $x = 5$, we have $L.H.S. = R.H.S.$
View full question & answer→Question 473 Marks
The sum of three consecutive odd numbers is $21$. Find the numbers.
AnswerLet the required numbers are $x, x + 2$ and $x + 4$
Then, $x + x + 2 + x + 4 = 21$
Or, $3x = 21 - 6$
$\Rightarrow\text{x}=\frac{15}{3}$
$x = 5$
So, the numbers are $5, (5 + 2 ) = 7$ and $(5 + 4) = 9$
View full question & answer→Question 483 Marks
Solve the following equation by trial and error method:
$\frac{\text{x}}{3}=4$
AnswerThe given equation is $\frac{\text{x}}{3}=4$
We guess and try several values of $x$ to find $L.H.S.$ and $R.H.S$. and stop when $L.H.S. = R.H.S.$
| x |
L.H.S. |
R.H.S. |
| $3$ |
$\frac{3}{3}=1$ |
$4$ |
| $6$ |
$\frac{6}{3}=2$ |
$4$ |
| $9$ |
$\frac{9}{3}=3$ |
$4$ |
| $12$ |
$\frac{12}{3}=4$ |
$4$ |
When $x = 12,$
we have $L.H.S. = R.H.S$
So $x = 12$ is the solution of the given equation. View full question & answer→Question 493 Marks
A wire of length $86\ cm$ is bent in the form of a rectangle such that its length is $7\ cm$ more than its breadth. Find the length and the breadth of the rectangle so formed.
AnswerLet breadth is $x \ cm$. and length is $(x + 7) \ cm$
Then, $2(x + x +7) = 86$
Or, $4x + 14 = 86$
$\Rightarrow 4x = 86 - 14$
$\Rightarrow\text{x}=\frac{72}{4}$
$x = 18$
So, the breadth of rectangle formed is $18\ cm$ and the length is $(18 + 7) = 25\ cm$
View full question & answer→