Answer :
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]
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]
