Question

Solve the inequality.
18 +2 10
x≤ ? or x>
[?]

Answer 1

`\left| 18+\cfrac{x}{2} \right|~ \geqslant ~ 10\implies \pm\left( 18+\cfrac{x}{2}\right)~ \geqslant ~ 10 \\\\[-0.35em] ~\dotfill`

`+\left( 18+\cfrac{x}{2}\right)~ \geqslant ~ 10\implies 18+\cfrac{x}{2}~ \geqslant ~ 10\implies \cfrac{x}{2}~ \geqslant ~ -8\implies \boxed{x~ \geqslant ~ -16} \\\\[-0.35em] ~\dotfill\\\\ -\left( 18+\cfrac{x}{2}\right)~ \geqslant ~ 10\implies 18+\cfrac{x}{2}~ \stackrel{ \stackrel{\textit{\\ormalsize notice}}{\downarrow } }{\leqslant} ~ -10 \\\\\\ \cfrac{x}{2}~ \leqslant ~ -28\implies \boxed{x~ \leqslant ~ -56}`

Answer 2

x≤-56 or X ≥-16

Explanation:

Isolate the variable by dividing each side