Which represents the solution set of [tex]$5(x + 5) \ \textless \ 85$[/tex]?

A. [tex]x \ \textless \ 12[/tex]
B. [tex]x \ \textgreater \ 12[/tex]
C. [tex]x \ \textless \ 16[/tex]
D. [tex]x \ \textgreater \ 16[/tex]



Answer :

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]