[3 marks sum]

Question 13 Marks

A natural number decreased by 7 is 12. Find the number.

Answer

Let the required number = x

Then x - 7 = 12

⇒ x - 7 + 7 = 12 + 7 (Adding 7 to both sides)

x = 19

∴ Required number = 19

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Question 23 Marks

Solve the following equation: 5x – 2x +15 = 27

Answer

5x – 2x +15 = 27
⇒ 3x + 15 = 27
⇒ 3x + 15 - 15 = 27 - 15 ...(Subtracting 15 from both sides)
⇒ 3x = 12
$\Rightarrow \frac{3 x }{3}=\frac{12}{3} \quad \ldots($ Dividing by 3$)$
$
\Rightarrow x=4
$

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Question 33 Marks

Solve the following equation : $3 \frac{2}{5}-y=2 \frac{1}{2}$

Answer

$3 \frac{2}{5}-y=2 \frac{1}{2}$
$\Rightarrow 3 \frac{2}{5}- y -3 \frac{2}{5}$
$=2 \frac{1}{2}-3 \frac{2}{5}..($subtracting $3 \frac{2}{5}$ from both sides$)$
$\Rightarrow-y=\frac{5}{2}-\frac{17}{5}$
$\Rightarrow \frac{25-34}{10}=\frac{-9}{10}$
$\Rightarrow y=\frac{9}{10}$

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Question 43 Marks

Solve the following equation: $x-2 \frac{1}{3}=5 \frac{1}{2}$

Answer

$x-2 \frac{1}{3}=5 \frac{1}{2}$
$\Rightarrow x -2 \frac{1}{3}+2 \frac{1}{3}=5 \frac{1}{2}+2 \frac{1}{3}..($Adding $2 \frac{1}{3}$ to both sides$)$
$\Rightarrow x=5 \frac{1}{2}+2 \frac{1}{3}=\frac{11}{2}+\frac{7}{3}$
$\Rightarrow \frac{33+14}{6}=\frac{47}{6}$
$\Rightarrow 7 \frac{5}{6}$

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Question 53 Marks

Solve the following equation : $\frac{y}{1.8}-2.1=-2.8$

Answer

$\frac{ y }{1.8}-2.1=-2.8$
$\Rightarrow \frac{ y }{1.8}-2.1+2.1$
$=-2.8+2.1($ Adding $2.1$ to both sides $)$
$\Rightarrow \frac{ y }{1.8}=-0.7$
$\Rightarrow \frac{ y }{1.8} \times 1.8$
$=-0.7 \times 1.8($ Multiplying by $1.8)$
$\therefore y=-1.26$

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Question 63 Marks

Solve the following equation : $\frac{ Z }{2.4}+3.6=5.1$

Answer

$\frac{ Z }{2.4}+3.6=5.1$
$\Rightarrow \frac{ z }{2.4}+3.6-3.6$
$=5.1-3.6 ($ Substracting $3.6$ from both sides $)$
$\Rightarrow \frac{ z }{2.4}=1.5$
$\Rightarrow \frac{ Z }{2.4} \times 2.4$
$=1.5 \times 2.4 ($Multiplying by $2.4)$
$\Rightarrow z=3.60$
$\therefore z=3.6$

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Question 73 Marks

Solve the following equation : $\frac{ x }{1.2}-6=1$

Answer

$\frac{ x }{1.2}-6=1$
$\Rightarrow \frac{ x }{1.2}-6+6=1+6 ($Adding $6$ to both sides $)$
$\Rightarrow \frac{ x }{1.2}=7$
$\Rightarrow \frac{ x }{1.2}=7 \times 1.2 ($ Multiplying by $1.2)$
$\therefore x=8.4$

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Question 83 Marks

Solve the following equation: 7y -18 = 17

Answer

7y -18 = 17
⇒ 7y - 18 + 18 = 17 + 18 (Adding 18 to both sides)
⇒ 7y = 35
$\Rightarrow \frac{7 y}{7}=\frac{35}{7} \quad$ (Dividing by 7 )
∴ y = 5

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Question 93 Marks

Solve the following equation: 3z + 2 = -4

Answer

3z + 2 = -4
⇒ 3z + 2 - 2 = - 4 - 2 (Substrating -2 from both sides)
⇒ 3z = - 6
$\Rightarrow \frac{3 z}{3}=\frac{-6}{3} \quad$ (Dividing by 3 )
∴ z = - 2

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Question 103 Marks

Solve the following equation: 4x + 4.9 = 6.5

Answer

4x + 4.9 = 6.5
⇒ 4x + 4.9 - 4.9 = 6.5 - 4.9
⇒ 4x = 1.6 (Substrating 4.9 from both sides)
$\Rightarrow \frac{4 x }{4}=\frac{1.6}{4} \quad$ (Dividing by 4 )
⇒ x = 0.4
∴ x = 0.4

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Question 113 Marks

Solve the following equation: 8y = 3- 3y

Answer

8y = 3- 3y
⇒ 18 - 3 = 3 - 3y - 3 (Substrating 3 from both sides)
⇒ 15 = - 3y
$\Rightarrow \frac{15}{-3}=\frac{-3 y}{-3} \quad$ (Dividing by -3 )
⇒ - 5 = y
∴ y = - 5

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Question 123 Marks

Solve the following equation $: -3x + 4 = 10$

Answer

$-3 x+4=10$
$\Rightarrow-3 x+4-4=10-4($ Substracting $4$ from bothsides $)$
$\Rightarrow-3 x=6$
$\Rightarrow \frac{-3 x}{-3}=\frac{6}{-3}($ Dividing by $-3t)$
$\therefore x=-2$

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Question 133 Marks

Solve the following equation : $\frac{y}{3}+7=2$

Answer

$\frac{ y }{3}+7=2$
$\Rightarrow \frac{ y }{3}+7-7$
$=2-7 \ldots ($ Substracting $7$ from both sides $)$
$\Rightarrow \frac{ y }{3}=-5$
$\Rightarrow \frac{ y }{3} \times 3$
$=-5 \times 3 . .($ Multiplying by $3)$
$\therefore y=-15$

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Question 143 Marks

Solve the following equation : $\frac{ X }{2}-3=5$

Answer

$\frac{ x }{2}-3=5$
$\Rightarrow \frac{ x }{2}-3+3=5+3 \ldots($ Adding $3$ to both sides $)$
$\Rightarrow \frac{ x }{2}=8$
$\Rightarrow \frac{ x }{2} \times 2=8 \times 2 . .($ Multiplying by $2)$
$\therefore x =16$

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Question 153 Marks

Solve the following equation: 48 z + 3.6 = 1.2

Answer

48 z + 3.6 = 1.2
⇒ 4.8z + 3.6 - 3.6 = 1.2 - 3.6 ...(Substracting 3.6 from both sides)
⇒ 4.8z = - 2.4
$\Rightarrow \frac{4.8 z }{4.8}=\frac{-2.4}{4.8} \quad$..(Dividing by 4.8)
$
\therefore z=\frac{-1}{2}=-0.5
$

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Question 163 Marks

Solve the following equation: 5y + 4.9 = 2.4

Answer

5y + 4.9 = 2.4
⇒ 5x + 4.9 - 4.9 = 2.4 - 4.9 ...(Substracting 4.9 from both sides)
⇒ 5y = - 2.5
$\Rightarrow \frac{5 y}{5}=\frac{2.5}{2} \quad$..(Dividing by 5$)$
∴ x = - 0.5

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Question 173 Marks

Solve the following equation: 5x – 2.4 = 4.9

Answer

5x – 2.4 = 4.9
⇒ 5x - 2.4 + 2.4 = 4.9 + 2.4 ...(Adding 2.4 to both sides)
⇒ 5x = 7.3
$\Rightarrow \frac{5 x }{5}=\frac{7.3}{5} \quad . .($ Dividing by 5)
∴ x = 1.46

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Question 183 Marks

Solve the following equation: $u +3 \frac{1}{4}=4 \frac{1}{3}$

Answer

$u+3 \frac{1}{4}=4 \frac{1}{3}$
$\Rightarrow u +\frac{13}{4}=\frac{13}{3}$
$\Rightarrow u +\frac{13}{4}-\frac{13}{4}=\frac{13}{3}-\frac{13}{4} \ldots($ Substracting $\frac{13}{4}$ from both sides$)$
$\Rightarrow u =\frac{52-39}{12}=\frac{13}{12}$
$\therefore u =\frac{13}{12}=1 \frac{1}{12}$

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Question 193 Marks

Solve the following equation : $\frac{3}{5} x +4=13$

Answer

$\frac{3}{5} x +4=13$
$\Rightarrow \frac{3}{5} x +4-4$
$=13-4 ($ subtracting $4$ from both sides$)$
$\Rightarrow \frac{3}{5} x =9$
$\Rightarrow \frac{3}{5} x \times \frac{5}{3}$
$=9 \times \frac{5}{3} \ldots ($ Multiplying by $\frac{5}{3})$
$\therefore x =15$

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Question 203 Marks

Solve the following equation: $3y \div 8 = 13$

Answer

$\Rightarrow \frac{3 y}{8}=13$
$\Rightarrow \frac{3 y}{8} \times 8=13 \times 8 \ldots( $Multiplying by $8)$
$\Rightarrow 3 y=104 \ldots .($ Dividing by $3)$
$\therefore y=\frac{104}{3}=34 \frac{2}{3}$

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Question 213 Marks

Solve the following equation: 3y + 8 = 13

Answer

3y + 8 = 13
⇒ 3y + 8 - 8 = 13 - 8 ...(Substracting 8 from both sides)
⇒ 3y = 5
$\Rightarrow \frac{3 y}{3}=\frac{5}{3} \quad \ldots .($ Dividing by 3$)$
$
\therefore y =\frac{5}{3}=1 \frac{2}{3}
$

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Question 223 Marks

Solve the following equation: 3y – 8 = 13

Answer

3y – 8 = 13
⇒ 3y - 8 + 8 = 13 + 8 ...(Adding 8 to both sides)
⇒ 3y = 21
$\Rightarrow \frac{3 y}{3}=\frac{21}{3} \quad \ldots .($ Dividing by 3$)$
∴ y = 7

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Question 233 Marks

Solve the following equation: 2x – 3 = 7

Answer

2x - 3 = 7
⇒ 2x - 3 + 3 = 7 + 3 ...(Adding 3 to both sides)
⇒ 2x = 10
$\Rightarrow \frac{2 x }{2}=\frac{10}{2} \ldots .($ Dividing by 2$)$
⇒ x = 2
∴ x = 5

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Question 243 Marks

Solve the following equation: 2x + 3 = 7

Answer

2x + 3 = 7
⇒ 2x + 3 - 3 = 7 - 3 ...(Subtracting 3 from both sides)
⇒ 2x = 4
$\Rightarrow \frac{2 x }{2}=\frac{4}{2} \ldots$. (Dividing by 2$)$
⇒ x = 2
∴ x = 2

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Question 253 Marks

A number decreased by 8 equals 26, find the number.

Answer

Let required number = A

∴ According to the sum:

x – 8 = 26

⇒ A = 26 + 8

⇒ A = 34

∴ Required number = 34

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Question 263 Marks

A whole number is increased by 7 and the new number so obtained is multiplied by 5; the result is 45. Find the whole number.

Answer

Let the required whole number = x
Then (x + 7) × 5 = 45
$\Rightarrow \frac{( x +7) \times 5}{5}=\frac{45}{5} \quad$ (Dividing by 5 )
⇒ x + 7 = 9
⇒ x = 9 - 7
x = 2
∴ Required whole number = 2

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Question 273 Marks

One fourth of a number added to one$-$ sixth of itself is $15.$ Find the number.

Answer

Let the required number $= x$
The $\frac{x}{4}+\frac{x}{6}=15$
$=\frac{3 x+2 x}{12}=15$
$\Rightarrow \frac{5 x}{12}=15$
$\Rightarrow x=\frac{15 \times 12}{5}$
$\Rightarrow x = 36$
$\therefore$ Required number $= 36$

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Question 283 Marks

Solve: (5x - 3) 4 = 3

Answer

(5x - 3) 4 = 3
$\Rightarrow \frac{5 x-3}{4}=3$
⇒ 5x - 3 = 3 × 4
⇒ 5x - 3 = 12
⇒ 5x = 12 + 3
⇒ 5x = 15
$\Rightarrow x=\frac{15}{5}=3$
∴ x = 3

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Question 293 Marks

Solve $: -3y – 2 = 10$

Answer

$-3 y-2=10$
$\Rightarrow-3 y=10+2$
$\Rightarrow-3 y=12$
$\Rightarrow y=\frac{12}{-3}$
$\Rightarrow y=-4$

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Question 303 Marks

Solve: $\frac{ X }{4}+3.6=-1.1$

Answer

$\frac{ x }{4}+3.6=-1.1$
$\Rightarrow \frac{ x }{4}=-1.1-3.6$
$\Rightarrow \frac{ x }{4}--4.7$
$\Rightarrow x = - 4.7 \times 4$
$\Rightarrow x = - 18.8$

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Question 313 Marks

Solve: $\frac{ z }{3}-1=-5$

Answer

$\frac{ z }{3}-1=-5$
$\Rightarrow \frac{ z }{3} \times 3-1 \times 3=-5 \times 3$
$\Rightarrow z - 3 = - 15$
$\Rightarrow z = - 15 + 3$
$\Rightarrow z = - 12$

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Question 323 Marks

Solve : $\frac{y}{2}-5=1$

Answer

$\frac{y}{2}-5=1$
$\Rightarrow \frac{y}{2} \times 2-5 \times 2=1 \times 2$
$\Rightarrow y - 10 = 2$
$\Rightarrow y = 2 + 10$
$\Rightarrow y = 12$

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Question 333 Marks

Solve $: 2x + 4.6 = 8$

Answer

$2x + 4.6 = 8$
$\Rightarrow 2x = 8 - 4.6$
$\Rightarrow 2x = 3.4$
$\Rightarrow x=\frac{3.4}{2}$
$\Rightarrow x=\frac{34}{2 \times 10}$
$\Rightarrow x=\frac{17}{10}=1.7$

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Question 343 Marks

Solve: $\frac{ z }{6}=-1 \frac{2}{3}$

Answer

$\frac{z}{6}=-1 \frac{2}{3}$
$\Rightarrow \frac{z}{6}=-\frac{5}{3}$
$\Rightarrow z \times 3=-5 \times 6$
$\Rightarrow z=\frac{-5 \times 6}{3}$
$\Rightarrow z=-10$

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Question 353 Marks

Solve: 3x + 5 + 2x + 6 + x = 4x + 21

Answer

3x + 5 + 2x + 6 + x = 4x + 21
⇒ 6x + 11 = 4x + 21
⇒ 6x - 4x = 21 - 11
⇒ 2x = 10
$\Rightarrow x=\frac{10}{2}$
⇒ x = 5

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Question 363 Marks

Solve: 18 - (2a - 12) = 8a

Answer

18 - (2a - 12) = 8a
⇒ 18 - 2a + 12 = 8a
⇒ - 2a - 8a = - 18 - 12
⇒ - 10a = - 30
$\Rightarrow a =\frac{-30}{-10}$
⇒ a = 3

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Question 373 Marks

Solve: 6x + 2 = 2x + 10

Answer

6x + 2 = 2x + 10
⇒ 6x - 2x = 10 - 2
⇒ 4x = 8
$\Rightarrow x=\frac{8}{4}$
⇒ x = 2

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Question 383 Marks

Solve: 4x - x + 5 = 8

Answer

4x - x + 5 = 8
⇒ 3x + 5 = 8
⇒ 3x = 8 - 5
⇒ 3x = 3
$\Rightarrow x=\frac{3}{3}=1$

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Question 393 Marks

Solve $: 4x + 2x = 3 + 5$

Answer

$4x + 2x = 3 + 5$
$\Rightarrow 6x = 8$
$\Rightarrow x=\frac{8}{6}$
$\Rightarrow x=\frac{4}{3}$
$\Rightarrow x=1 \frac{1}{3}$

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Question 403 Marks

Solve : $\frac{m}{4}-4.6=-3.1$

Answer

$\frac{ m }{4}-4.6=-3.1$
$\Rightarrow \frac{ m }{4}=-3.1+4.6$
$\Rightarrow \frac{ m }{4}=1.5$
$\Rightarrow m =1.5 \times 4$
$\Rightarrow m =6$

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Question 413 Marks

Solve : $\frac{b}{1.6}+3=-2.5$

Answer

$\frac{ b }{1.6}+3=-2.5$
$\Rightarrow \frac{ b }{1.6}=-2.5-3$
$\Rightarrow \frac{ b }{1.6}=-5.5$
$\Rightarrow b =-5.5 \times 1.6$
$\Rightarrow b =-8.80$

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Question 423 Marks

Solve : $\frac{ a }{2.4}-5=2.4$

Answer

$\frac{ a }{2.4}-5=2.4$
$\Rightarrow \frac{ a }{2.4}=2.4+5$
$\Rightarrow \frac{ a }{2.4}=7.4$
$\Rightarrow a =7.4 \times 2.4$
$\Rightarrow a =17.76$

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Question 433 Marks

Solve : $\frac{x}{3}-5=2$

Answer

$\frac{ x }{3}-5=2$
$\Rightarrow \frac{ x }{3}=2+5$
$\Rightarrow \frac{ x }{3}=7$
$\Rightarrow x = 7 \times 3$
$\Rightarrow x = 21$

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Question 443 Marks

Solve: 6y + 4 = - 4.4

Answer

6y + 4 = - 4.4
⇒ 6y = - 4.4 - 4.0
⇒ 6y = - 8.4
$\Rightarrow y=-\frac{8.4}{6}$
⇒ y = - 1.4

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Question 453 Marks

Solve: 2.4x - 3 = 4.2

Answer

2.4x - 3 = 4.2
⇒ 2.4x = 4.2 + 3
⇒ 2.4x = 7.2
$\Rightarrow x=\frac{7.2}{2.4}$
⇒ x = 3

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Question 463 Marks

Solve $: 7m - 1 = 20$

Answer

$7 m -1=20$
$\Rightarrow 7 m =20+1$
$\Rightarrow 7 m =21$
$\Rightarrow m =\frac{21}{7}$
$\Rightarrow m =3$

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Question 473 Marks

Solve $: 2z + 3 = - 19$

Answer

$2 z+3=-19$
$\Rightarrow 2 z=-19-3$
$\Rightarrow 2 z=-22$
$\Rightarrow z=\frac{-22}{2}$
$\Rightarrow z=-11$

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Question 483 Marks

Solve $: 4a - 3 = - 27$

Answer

$4 a-3=-27$
$\Rightarrow 4 a=-27+3$
$\Rightarrow 4 a=-24$
$\Rightarrow a=\frac{-24}{4}$
$\Rightarrow a=-6$

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Question 493 Marks

Solve: 5p + 4 = 29

Answer

5p + 4 = 29
⇒ 5p = 29 - 4
⇒ 5p = 25
$\Rightarrow p=\frac{25}{5}$
⇒ p = 5

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Question 503 Marks

Solve $: 3y - 2 = 1$

Answer

$3 y-2=1$
$\Rightarrow 3 y=1+2$
$\Rightarrow 3 y=3$
$\Rightarrow y=\frac{3}{3}$
$\Rightarrow y=1$

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MATHS [3 marks sum]

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