Question

Solve the inequality, write the solution set and then represent the solution on number line.

5$\geq$x/2+3$\geq$-1

Please Help Me

Answer 1

       $\underline{\bold{Solution:}}$

       $\text{The given inequality is }5\geq \dfrac{x}{2}+ 3 \geq -1$

       $\text{Substracting 3 on all sides}$

$\implies5 - 3\geq \dfrac{x}{2}+ 3 - 3\geq -1 - 3$

       $\text{Simplifying...}$

$\implies2\geq \dfrac{x}{2}\geq -4$

       $\text{Multiplying 2 on all sides}$

$\implies2(2)\geq \dfrac{x}{2}(2)\geq -4(2)$

       $\text{Simplifying...}$

$\implies4\geq x\geq -8$

       $\text{Representing the solution on the number line...}$