Question

Solve the following inequality and write the solution set using interval notation

1. -9<2x+7<_19​

Answer 1

To solve the inequality -9 < 2x + 7 <= 19, subtract 7 and divide by 2 to find the lower bound and subtract 7 and divide by 2 to find the upper bound. The solution set in interval notation is (-8, 6].

Step-by-step explanation:

To solve the inequality -9 < 2x + 7 ≤ 19, we need to tackle it in two parts:

1. First, solve -9 < 2x + 7 to find the lower bound.
2. Next, solve 2x + 7 ≤ 19 to find the upper bound.

For the first part, subtract 7 from both sides and divide by 2 to isolate x:

-9 - 7 < 2x + 7 - 7

-16 < 2x

-8 < x

For the second part, subtract 7 from both sides:

2x + 7 - 7 ≤ 19 - 7

2x ≤ 12

Divide by 2:

x ≤ 6

Combining the two solutions, we have:

-8 < x ≤ 6

This is the solution set in interval notation. The answer is (-8, 6].