Answer:
[tex]\textsf{D. }x\leq-2[/tex]
Step-by-step explanation:
Given inequality: [tex]3(x+2)\leq5(-2-x)[/tex]
Step 1: Distribute [tex]3[/tex] and [tex]5[/tex] through the parentheses.
[tex]\implies 3(x)+3(2)\leq5(-2)+5(-x)[/tex]
[tex]\implies 3x+6\leq-10-5x[/tex]
Step 2: Subtract [tex]6[/tex] from both sides.
[tex]\implies 3x+6-6\leq-10-6-5x[/tex]
[tex]\implies 3x\leq-16-5x[/tex]
Step 3: Add [tex]5x[/tex] to both sides.
[tex]\implies 3x+5x\leq-16-5x+5x[/tex]
[tex]\implies 8x\leq-16[/tex]
Step 4: Divide both sides by [tex]8[/tex].
[tex]\implies \dfrac{8x}{8}\leq\dfrac{-16}{8}[/tex]
[tex]\implies x\leq-2[/tex]
