Sure, let's solve the inequality [tex]\(5(x + 5) < 85\)[/tex] step by step.
1. Start with the given inequality:
[tex]\[ 5(x + 5) < 85 \][/tex]
2. Distribute the 5 on the left side:
[tex]\[ 5 \cdot x + 5 \cdot 5 < 85 \][/tex]
[tex]\[ 5x + 25 < 85 \][/tex]
3. Subtract 25 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ 5x + 25 - 25 < 85 - 25 \][/tex]
[tex]\[ 5x < 60 \][/tex]
4. Divide both sides by 5 to solve for [tex]\(x\)[/tex]:
[tex]\[ \frac{5x}{5} < \frac{60}{5} \][/tex]
[tex]\[ x < 12 \][/tex]
So, the solution set of the inequality [tex]\(5(x + 5) < 85\)[/tex] is:
[tex]\[ x < 12 \][/tex]
Thus, the correct answer is:
[tex]\[ x < 12 \][/tex]
