Solve. 5 < x - 2 < 11

a. 5 < x < 11
b. 7 < x < 13
c. 7 < x < 11
d. 5 < x < 16

My answer is b. Can you check my work?

looks good

Ok, thanks!

To solve the inequality 5 < x - 2 < 11, we'll break it down into two separate inequalities and solve them individually.

First, let's solve for the lower bound: 5 < x - 2

Adding 2 to both sides of the inequality, we get 5 + 2 < x - 2 + 2, which simplifies to 7 < x.

So for the lower bound, x > 7.

Next, let's solve for the upper bound: x - 2 < 11

Adding 2 to both sides of the inequality, we get x - 2 + 2 < 11 + 2, which simplifies to x < 13.

So for the upper bound, x < 13.

Combining both results, we have 7 < x < 13.

Comparing the solution to the answer choices, the correct choice is b. Therefore, your answer is correct. Well done!