Question 12 Marks
List the elements of the solution set of the inequation
-3 < x – 2 ≤ 9 – 2x; x ∈ N.
Answer-3 < $x$ - 2 $\leq$ 9 - 2x
-3 < $x$ - 2 and x -2 $\leq$ 9 - 2x
-1 < $x$ $\leq$ $\frac{11}{3}$
Since, $x \in N$
$\therefore$ Solution set $=\{1,2,3\}$
View full question & answer→Question 22 Marks
Represent the solution of the given inequalities on the real number line
$\frac{2 x+5}{3}>3 x-3$
Answer$\frac{2 x+5}{3}>3 x-3$
$ 2 x+5>9 x-9 $
$ -7 x>-14 $
$ x<2$
The solution on number line is:
View full question & answer→Question 32 Marks
Represent the solution of the given inequalities on the real number line
$1+x \geq 5 x-11$
Answer$1+x \geq 5 x-11 $
$ 12 \geq 4 x $
$3 \geq x$
The solution on number line is:
View full question & answer→Question 42 Marks
Represent the solution of the given inequalities on the real number line
$2 - 3x > 7 - 5x$
Answer$2-3 x>7-5 x $
$ 2 x>5 $
$ x>\frac{5}{2} $
$ x>2.5$
The solution on number line is:
View full question & answer→Question 52 Marks
Represent the solution of the given inequalities on the real number line
$x+3 \leq 2 x+9$
Answer$x+3 \leq 2 x+9$
$-6 \leq x$
The solution on number line is
View full question & answer→Question 62 Marks
Represent the solution of the given inequalities on the real number line
$7-x \leq 2-6 x$
Answer$7-x \leq 2-6 x$
$ 5 x \leq-5$
$ x \leq-1$
The solution on number line is:
View full question & answer→Question 72 Marks
Represent the solution of the given inequalities on the real number line
4x - 1 > x + 11
Answer$4 x-1>x+11$
$3 x>12$
$x>4$
The solution on number line is
View full question & answer→Question 82 Marks
For the given inequations graph the solution set on the real number line
$x-1<3-x \leq 5$
Answer$x-1<3-x \leq 5 $
$ x-1<3-x \text { and } 3-x \leq 5$
$ 2 x<4 \text { and }-x \leq 2$
$x<2 \text { and } x \geq-2$
The solution set on the real number line is
View full question & answer→Question 92 Marks
For the given inequations graph the solution set on the real number line $-4 < 3x - 1 < 8$
Answer$-4 \leq 3 x-1<8 $
$ -4 \leq 3 x-1 \text { and } 3 x-1<8$
$ -1 \leq x \text { and } x <3$
The solution set on the real number line is
View full question & answer→Question 102 Marks
Solve
$\frac{2 x+3}{3} \geq \frac{3 x-1}{4}$ where $x$ is a positive even integer.
Answer$\frac{2 x+3}{3} \geq \frac{3 x-1}{4} $
$8 x+12 \geq 9 x-3$
$x \geq-15 $
$ x \leq 15$
Since x is positive even integer
$\therefore$ Solution set $= {2, 4, 6, 8, 10, 12, 14}$
View full question & answer→Question 112 Marks
Solve
$\frac{x}{2}+5 \leq \frac{x}{3}+6$ where $x$ is a positive odd integer.
Answer$\frac{x}{2}+5 \leq \frac{x}{3}+6 $
$\frac{x}{2}-\frac{x}{3} \leq 6-5$
$\frac{x}{6} \leq 1$
$ x \leq 6$
Since $x$ is a positive odd integer
$\therefore$ Solution set $= {1, 3, 5}$
View full question & answer→Question 122 Marks
Represent the following in-equalities on real number line :
−5 < × ≤ −1
Answer−5 < × ≤ −1
Solution on number line is :
View full question & answer→Question 132 Marks
Given A = {x: -1 < x ≤ 5, x ∈ R} and B = {x: -4 ≤ x < 3, x ∈ R}
Represent on different number lines:
A' ∩ B
AnswerNumbers which belong to B but do not belong to A = B - A
A' ∩ B = {x : -4 <= x <= -1 , x ∈ R}
It can be represented on a number line as
View full question & answer→Question 142 Marks
Illustrate the set {x: -3 ≤ x < 0 or x > 2, x ∈ R} on the real number line.
AnswerGraph of solution set of -3 ≤ x < 0 or x > 2
= Graph of points which belong to -3 ≤ x < 0 or x > 2 or both
Thus, the required graph is:
View full question & answer→Question 152 Marks
Represent the following inequalities on real number lines
$8 \geq x>-3$
Answer$8 \geq x>-3$
Solution on number line is
View full question & answer→Question 162 Marks
Represent the following inequalities on real number lines
$-2 \leq x<5$
Answer$-2 \leq x<5$
Solution on number line is
View full question & answer→Question 172 Marks
Represent the following inequalities on real number lines-4 < x < 4
Answer-4 < x < 4
Solution on number line is
View full question & answer→Question 182 Marks
Represent the following inequalities on real number lines
$2(2 x-3) \leq 6$
Answer$2(2 x-3) \leq 6 $
$2 x-3 \leq 3 $
$2 x \leq 6$
$ x \leq 3$
Solution on number line is
View full question & answer→Question 192 Marks
Represent the following inequalities on real number lines $3x + 1 >= -5$
Answer$3 x+1 \geq-5 $
$ 3 x \geq-6 $
$x \geq-2$
Solution on number line is
View full question & answer→Question 202 Marks
Solve and graph the solution set of $:x + 5 ≥ 4(x - 1)$ and $3 - 2x < -7 ; x \in R .$
Answer$x+5 \geq 4(x-1)$ and $3-2 x<-7$
$9 \geq 3 x \text { and }-2 x<-10$
$ 3 \geq x \text { and } x>5$
$\therefore$ Solution set = Empty set
View full question & answer→Question 212 Marks
Solve and graph the solution set of $:2x – 9 \leq 7$ and $3x + 9 > 25, x \in I$
Answer$2 x-9 \leq 7 \text { and } 3 x+9>25 $
$2 x \leq 16 \text { and } 3 x>16 $
$x \leq 8 \text { and } x>5 \frac{1}{3}$
$\therefore$ Solutionset$=\left\{5 \frac{1}{3}< x \leq 8, x \in I\right\} = {6,7,8}$
The required graph on number line is
View full question & answer→Question 222 Marks
Solve and graph the solution set of $:2x – 9 < 7$ and $3x + 9 \leq 25, x \in R$
Answer$2 x-9<7 \text { and } 3 x+9 \leq 25 $
$2 x>16 \text { and } 3 x \leq 16$
$x < 8$ and $x \Leftarrow 5 1/3$
$\therefore$ Solution set $= \{x \Leftarrow 5 1/3, x \in R\}$
The required graph on number line is:
View full question & answer→Question 232 Marks
Solve the following inequation and graph the solution set on the number line:
2x – 3 < x + 2 ≤ 3x + 5, x ∈ R.
Answer2x -3 < x +2 $\leq$ 3x + 5
2x - 3 < x + 2 amd x + 2 $\leq$ 3x + 5
x < 5 and -3 $\leq$ 2x
x < 5 and -1.5 $\leq$ x
solution set = {-1.5 $\leq$ x < 5}
The solution set can be graphed on the number line as:
View full question & answer→Question 242 Marks
Represent the following inequalities on real number lines $2x - 1 < 5$
Answer$2 x-1<5$
$ 2 x<6 $
$x<3$
Solution on number line is
View full question & answer→Question 252 Marks
If 5x – 3 ≤ 5 + 3x ≤ 4x + 2, express it as a ≤ x ≤ b and then state the values of a and b.
Answer5x – 3 ≤ 5 + 3x ≤ 4x + 2
5x – 3 ≤ 5 + 3x and 5 + 3x ≤ 4x + 2
2x ≤ 8 and -x ≤ -3
x ≤ 4 and x ≥ 3
Thus, 3 ≤ x ≤ 4.
Hence, a = 3 and b = 4
View full question & answer→Question 262 Marks
Find the largest value of $x$ for which $2(x – 1) \leq 9 – x$ and $x \in W.$
Answer$2(x-1) \leq 9-x $
$ 2 x-2 \leq 9-x $
$ 2 x+x \leq 9+2$
$ 3 x \leq 11 $
$x \leq \frac{11}{3} $
$ x \leq 3.67$
Since, $x \in W$, thus the required largest value of $x$ is $3 .$
View full question & answer→Question 272 Marks
Find the smallest value of $x$ for which $5-2 x <5 \frac{1}{2}-\frac{5}{3} x$ where $x$ is interger
Answer$5-2 x <5 \frac{1}{2}-\frac{5}{3} x$
$-2 x+\frac{5}{3} x <\frac{11}{2}-5$
$ \frac{- x }{3}<\frac{1}{2}$
$ - x <\frac{3}{2}$
$ x>-1.5$
Thus, the required smallest value of $x$ is $-1.$
View full question & answer→Question 282 Marks
If the replacement set is the set of real numbers solve
$\frac{x+3}{8}<\frac{x-3}{5}$
Answer$\frac{x+3}{8}<\frac{x-3}{5} $
$5 x+15<8 x-24$
$ 5 x-8 x<-24-15 $
$-3 x<-39 $
$ x>13$
Since the replacement set of real numbers
$\therefore$ Solution set $=\{x: x \in R$ and $x>13\}$
View full question & answer→Question 292 Marks
If the replacement set is the set of real numbers solve
$5+\frac{x}{4}>\frac{x}{5}+9$
Answer$5+\frac{x}{4}>\frac{x}{5}+9 $
$ \frac{x}{4}-\frac{x}{5}>9-5$
$ \frac{x}{20}>4 $
$ x>80$
Since the replacement set of real numbers.
$\therefore$ Solution set = $\{x: x \in R$ and $x>80\}$
View full question & answer→Question 302 Marks
If the replacement set is the set of real numbers solve
$8-3 x \leq 20$
Answer$8-3 x \leq 20$
$ -3 x \leq 20-8 $
$ -3 x \leq 12$
$x \geq-4$
Since the replacement set of real numbers.
$\therefore$ Solution set $=\{x: x \in R$ and $x \geq-4\}$
View full question & answer→Question 312 Marks
If the replacement set is the set of real numbers solve
$-4 x \geq-16$
Answer$-4 x \geq-16$
$x<4$
Since the replacement set of real numbers
$\therefore$ Solution set $=\{x: x \in R$ and $x \leq 4\}$
View full question & answer→Question 322 Marks
If $25 – 4x \leq 16,$ find:(1) the smallest value of x, when x is a real number,
(2) the smallest value of x, when x is an integer.
Answer$25-4 x \leq 16$
$-4 x \leq 16-25$
$-4 x \leq-9$
$x \geq \frac{9}{4}$
$x \geq 2.25$
(1) The smallest value of x, when x is a real number, is $2.25.$
(2) The smallest value of x, when x is an integer, is $3.$
View full question & answer→Question 332 Marks
Solve the inequation:
3 – 2x ≥ x – 12 given that x ∈ N.
Answer3 – 2x ≥ x – 12
-2x – x ≥ -12 – 3
-3x ≥ -15
x ≤ 5
Since, x ∈ N, therefore,
Solution set = {1, 2, 3, 4, 5}
View full question & answer→Question 342 Marks
If the replacement set is the set of whole numbers solve
$18 \leq 3 x-2$
AnswerSince the replacement set = W(set of whole numbers)
$\therefore$ Solution set $= {7, 8, 9, …}$
$18 \leq 3 x-2 $
$ 18+2 \leq 3 x$
$ 20 \leq 3 x $
$x \geq \frac{20}{3}$
View full question & answer→Question 352 Marks
If the replacement set is the set of whole numbers solve
$x-\frac{3}{2}<\frac{3}{2}-x$
Answer$x-\frac{3}{2}<\frac{3}{2}-x $
$ x+x<\frac{3}{2}+\frac{3}{2}$
$ 2 x<3$
$ x<\frac{3}{2}$
Since, the replacement set $= W$ (set of whole numbers)
$\therefore$ Solution set $= {0, 1}$
View full question & answer→Question 362 Marks
If the replacement set is the set of whole numbers solve
$7-3 x \geq-\frac{1}{2}$
Answer$7-3 x \geq-\frac{1}{2} $
$ -3 x \geq-\frac{1}{2}-7$
$ -3 x \geq-\frac{15}{2} $
$ x \leq \frac{5}{2}$
Since, the replacement set $= W$ (set of whole numbers)
$\therefore$ Solution set $= \{0, 1, 2\}$
View full question & answer→Question 372 Marks
If the replacement set is the set of whole numbers solve
8 - x > 5
Answer8 – x > 5
– x > 5 – 8
– x > -3
x < 3
Since, the replacement set = W (set of whole numbers)
⇒ Solution set = {0, 1, 2}
View full question & answer→Question 382 Marks
If the replacement set is the set of whole numbers solve:
3x - 1 > 8
Answer3x – 1 > 8
3x > 8 + 1
x > 3
Since, the replacement set = W (set of whole numbers)
⇒ Solution set = {4, 5, 6, …}
View full question & answer→Question 392 Marks
If the replacement set is the set of whole numbers, solve :
$x+7 \leq 11$
Answerx + 7 ≤ 11
x ≤ 11 – 7
x ≤ 4
Since, the replacement set = W (set of whole numbers)
⇒ Solution set = {0, 1, 2, 3, 4}
View full question & answer→Question 402 Marks
If x ∈ N, find the solution set of inequations.
3x – 2 < 19 – 4x
Answer3x – 2 < 19 – 4x
3x + 4x < 19 + 2
7x < 21
x < 3
Since, x ∈ N, therefore solution set is {1, 2}.
View full question & answer→Question 412 Marks
If x ∈ N, find the solution set of inequations.
5x + 3 ≤ 2x + 18
Answer5x + 3 ≤ 2x + 18
5x – 2x ≤ 18 – 3
3x ≤ 15
x ≤ 5
Since, x ∈ N, therefore solution set is {1, 2, 3, 4, 5}.
View full question & answer→Question 422 Marks
Given $x \in$ {whole numbers}, find the solution set of $: -1 ≤ 3 + 4x < 23$
Answer$-1 \leq 3+4 x<23 $
$\Rightarrow-1 \leq 3=4 x \text { and } 3+4 x<23 $
$ \Rightarrow-4 \leq 4 x \text { and } 4 x<20 $
$ \Rightarrow x \geq-1 \text { and } x<5$
Sin cex $\in\{$ Whole number $\}$
$\therefore$ Solution set $=\{0,1,2,3,4\}$
View full question & answer→Question 432 Marks
Given x ∈ {integers}, find the solution set of $:-5 ≤ 2x – 3 < x + 2$
Answer$-5<=2 x -3< x +2$
$ \Rightarrow-5 \leq 2 x-3 \text { and } 2 x -3< x +2$
$ \Rightarrow-5+3 \leq 2 x \text { and } 2 x-x<2+3 $
$ \Rightarrow-2 \leq 2 x \text { and } x <5$
Since $x \in\{$ integer $\}$
$\therefore$ Solution set $=\{-1,0,1,2,3,4\}$
View full question & answer→Question 442 Marks
Solve the inequation $12+1 \frac{5}{6} \times \leq 5+3 x$ and $x \in R$
Answer$12+1 \frac{5}{6} \times \leq 5+3 x $
$\frac{11}{6} x-3 x \leq 5-12$
$ \frac{-7}{6} x \leq-7 $
$x \geq 6$
$\therefore$ Solutionset $\{ x : x \in R$ and $x \geq 6\}$
View full question & answer→