To solve the inequality [tex]\(5(x + 5) < 85\)[/tex], let's proceed step-by-step.
1. Distribute the 5:
[tex]\[
5(x + 5) = 5x + 25
\][/tex]
So, the inequality becomes:
[tex]\[
5x + 25 < 85
\][/tex]
2. Isolate the term with the variable x:
Subtract 25 from both sides of the inequality to begin isolating [tex]\(x\)[/tex]:
[tex]\[
5x + 25 - 25 < 85 - 25
\][/tex]
Simplifying, we get:
[tex]\[
5x < 60
\][/tex]
3. Solve for x:
Now, divide both sides by 5 to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{5x}{5} < \frac{60}{5}
\][/tex]
Simplifying, we get:
[tex]\[
x < 12
\][/tex]
Therefore, the solution set for the inequality [tex]\(5(x + 5) < 85\)[/tex] is:
[tex]\[
x < 12
\][/tex]
So, the correct answer is:
[tex]\[
x < 12
\][/tex]
