# Solve the inequality and represent the solution graphically on number line . $5x + 1 > -24; 5x -1 < 24$

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

Toolbox:
• 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:
edited Aug 4, 2014 by meena.p