To solve the given inequality [tex]\( 2x + 7 \leq -13 \)[/tex], follow these steps:
1. Start by isolating the term containing [tex]\( x \)[/tex]. To do that, subtract 7 from both sides of the inequality:
[tex]\[
2x + 7 - 7 \leq -13 - 7
\][/tex]
Simplifying this, we get:
[tex]\[
2x \leq -20
\][/tex]
2. Next, we need to solve for [tex]\( x \)[/tex]. Since [tex]\( x \)[/tex] is being multiplied by 2, we divide both sides of the inequality by 2 to isolate [tex]\( x \)[/tex]:
[tex]\[
\frac{2x}{2} \leq \frac{-20}{2}
\][/tex]
Simplifying, we obtain:
[tex]\[
x \leq -10
\][/tex]
So, the solution to the inequality [tex]\( 2x + 7 \leq -13 \)[/tex] is [tex]\( x \leq -10 \)[/tex].
From the given options, the correct answer is:
(D) [tex]\( x \leq -10 \)[/tex]
