$\begin{array}{1 1}(A)\;[\frac{-80}{3},\frac{-10}{3}]\\(B)\;(-5,5)\\(C)\;(-23,2]\\(D)\;[2,3]\end{array} $

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- 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 $5x+1 > -24$

Adding $-1$ to both sides of inequalities $=> 5x > -25$

Dividing by 5 on both sides $=> x > -5$ -------(1)

Step 2:

The second inequality is $5x -1 <24$

Adding 1 on both sides of inequality

$=> 5x <25$

Dividing by 5 on both sides

=> $ x < 5$ -------(2)

Step 3:

From (1) and (2) we see that all numbers greater than -5 and less than 5 are solutions of given system of inequalities .

The solution set is $(-5,5)$

The solution is represented graphically on number line as:

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