Let's go through each inequality step-by-step to find which one is solved by subtracting 5 from both sides and then dividing by 2.
### Option 1: [tex]\(2x - 5 = 15\)[/tex]
1. Start with the inequality:
[tex]\[
2x - 5 = 15
\][/tex]
2. Add 5 to both sides to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
2x - 5 + 5 = 15 + 5 \implies 2x = 20
\][/tex]
3. Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{2x}{2} = \frac{20}{2} \implies x = 10
\][/tex]
This equation does not match the criteria as we needed to subtract 5 first, but we actually added 5 in this case.
### Option 2: [tex]\(2x + 5 > 15\)[/tex]
1. Start with the inequality:
[tex]\[
2x + 5 > 15
\][/tex]
2. Subtract 5 from both sides:
[tex]\[
2x + 5 - 5 > 15 - 5 \implies 2x > 10
\][/tex]
3. Divide both sides by 2:
[tex]\[
\frac{2x}{2} > \frac{10}{2} \implies x > 5
\][/tex]
We subtracted 5 and then divided by 2, so this inequality fits the criteria.
### Option 3: [tex]\(2x + 5 = 15\)[/tex]
1. Start with the inequality:
[tex]\[
2x + 5 = 15
\][/tex]
2. Subtract 5 from both sides:
[tex]\[
2x + 5 - 5 = 15 - 5 \implies 2x = 10
\][/tex]
3. Divide both sides by 2:
[tex]\[
\frac{2x}{2} = \frac{10}{2} \implies x = 5
\][/tex]
This equation also involves subtracting 5 and dividing by 2, but it resolves into an equation [tex]\(x = 5\)[/tex] instead of an inequality.
### Option 4: [tex]\(2x - 5 > 15\)[/tex]
1. Start with the inequality:
[tex]\[
2x - 5 > 15
\][/tex]
2. Add 5 to both sides to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
2x - 5 + 5 > 15 + 5 \implies 2x > 20
\][/tex]
3. Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{2x}{2} > \frac{20}{2} \implies x > 10
\][/tex]
This inequality also fits the criteria as we subtracted 5 and then divided by 2.
### Conclusion
The given question asks for the inequality solved by subtracting 5 from both sides and then dividing by 2. Comparing the steps:
The correct answer is: [tex]\(2x - 5 > 15\)[/tex]
Thus, the inequality that is solved by subtracting 5 from both sides and then dividing by 2 is:
\[
\boxed{4}
