Sure, I'll guide you through the steps to solve the inequality [tex]\(16x - 7 \leq -71\)[/tex].
1. Start with the given inequality:
[tex]\[
16x - 7 \leq -71
\][/tex]
2. Isolate the term with [tex]\(x\)[/tex]:
- To do that, add 7 to both sides of the inequality to get rid of the constant term on the left-hand side.
[tex]\[
16x - 7 + 7 \leq -71 + 7
\][/tex]
- Simplifying this, we get:
[tex]\[
16x \leq -64
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
- To isolate [tex]\(x\)[/tex], divide both sides of the inequality by 16.
[tex]\[
\frac{16x}{16} \leq \frac{-64}{16}
\][/tex]
- Simplifying the fractions, we get:
[tex]\[
x \leq -4
\][/tex]
So, the solution set of the inequality [tex]\(16x - 7 \leq -71\)[/tex] is:
[tex]\[
x \leq -4
\][/tex]
