ML AGGARWAL CLASS 7 Chapter 9 Linear Equations and Inequalities Exercise 9.3

 

Exercise: 9.3

Question 1

i) x <-2

Replacement sent {$-5,-3,-1,0,1,3,4$}

Solutin set { -5, -3}

 

ii) x>1

Replacement set $\{-5,-3,-1,0,1,3,4\}$

Solution set $\{3,4\}$

iii) $x \geqslant-1$

Replacement set $\{-5,-3,-1,0,1,3,4\}$

Solution set $\{-1,0,1,3,4\}$

iv) $-5<x<3$

Replacement set $\{-5,-3,-1,0,1,3,4\}$

Solution set $\{-3,-1,0,1\}$

v) $-3 \leq x<4$

Replacement set $\{-5,-3,-1,0,1,3,4\}$

Solution set $\{-3,-1,0,1,3\}$

vi) $0 \leq x<7$

Replacement set $\{-5,-3,-1,0,1,3,4\}$

solution set $\{0,1,3,4\}$

Question 2

(i) $\begin{aligned} & x \leq 3 \\ & \text { Solution set }=\{1,2,3\} \end{aligned}$

(Diagram should be added)

ii) $x<4$

Solution set $=\{0,1,2,3\}$

(Diagram should be added)

iii) $-2 \leq x<4$

Solution set : $\{-2,-1,0,1,2,3\}$

(Diagram should be added)

iv) $-3 \leqslant x<2$

Solution set $=\{-3,-2,-1,0,1\}$

(Diagram should be added)

Question 3

(i)

 $\begin{aligned} 4-x>-2 & \\-4+4-x &>-2+(-4) \\-x &>-6 \\ x &<6 \end{aligned}$ Add both side $(-4)$

Solution Set = $\{1,2,3,4,5\}$

(Diagram should be added)

ii) $3 x+1 \leq 8$

$3 x+1-1 \leq$ 8-1

$3 x \leq 7$

$x \leq 7 / 3$

Solution set $=\{0,1,2\}$

(Diagram should be added)

Question 4

$3-4 x<x-12 \quad x \in\{-1,0,1,2,3,4,5,6,7\}$

$3-4 x-3<x-12-3 \quad$ Add $(-3)$ on both side

-4 x<x-15

$-4 x-x<x-15-x$ Add $(-x)$ on both side

$\begin{aligned}-5 x &<-15 \\ x & \geq 15 / 5 \\ x &>3 \end{aligned}$

Solution set $=\{4,5,6,7\}$

Question 5

$-7<4 x+1 \leq 23$

$-7-1<4 x+1-1 \leq 23-1$ Add $(-1)$ on both side

$-8<4 x \leq 22$

$-\frac{8}{4}<\frac{4 x}{4} \leq \frac{22}{4}$ Divide $(4)$ on both side

$-2<x \leq 11 / 2$

Solution set $\{-1,0,1,2,3,4,5\}$