Let's solve the inequality [tex]\(4x + 4 \leq 9x + 8\)[/tex] step-by-step to understand which of the given options is equivalent to the inequality.
1. Write down the given inequality:
[tex]\[
4x + 4 \leq 9x + 8
\][/tex]
2. Subtract [tex]\(4x\)[/tex] from both sides to begin isolating the variable [tex]\(x\)[/tex]:
[tex]\[
4 \leq 5x + 8
\][/tex]
3. Subtract 8 from both sides to further isolate the term with [tex]\(x\)[/tex]:
[tex]\[
4 - 8 \leq 5x
\][/tex]
4. Simplify the left side:
[tex]\[
-4 \leq 5x
\][/tex]
5. Divide both sides by 5 to solve for [tex]\(x\)[/tex]:
[tex]\[
-\frac{4}{5} \leq x
\][/tex]
This simplifies to:
[tex]\[
x \geq -\frac{4}{5}
\][/tex]
So the inequality [tex]\(4x + 4 \leq 9x + 8\)[/tex] is equivalent to [tex]\(x \geq -\frac{4}{5}\)[/tex].
Thus, the correct answer is:
[tex]\[
x \geq -\frac{4}{5}
\][/tex]
