$\begin{array}{1 1}(A)\;(-1,7) \\(B)\;(-5,5)\\(C)\;(-23,2]\\(D)\;[2,3]\end{array} $

- Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality.
- Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality.
- If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e $ '>'$ sign changes to $'<' $ and $'<'$ changes $'>'$ .
- To represent solution of linear inequality involving one variable on a number line, if the inequality involves $\geq $ or $\leq$ are draw filled circle (0) on the number is included in the solution set.
- If the inequality involves $'>'$ or $'<'$ we draw open circle (0) on the number line to indicate the number is excluded from the solution set.

Step 1:

The first inequality is $2(x-1) < x+5$

$=> 2x-2 < x+5 $

Subtracting x from both sides of inequality and adding 2 on both sides of inequality

$=> 2x -x -2+2 < x -x +5+2$

$=> x < 7$-----(1)

Step 2:

The second inequality is $3(x+2) > 2-x$

$=> 3x+6 > 2-x$

Adding x on both sides of the inequality and subtracting 6 from both sides of inequality .

$=> 3x+6 +x-6 > 2-x +x-6$

$=> 4x> -4$

Dividing by 4 on both sides of inequalities $=> x >-1$-----(2)

Step 3:

From (1) and (2) we conclude that all numbers greater than -1 and less than T are solutions to the given inequality

The solution set is $(-1,7)$

The solution is represented graphically as the number line as

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