Question

Solve the inequality.
22 − 2 x <38
Which inequality represents the solutions to this inequality?
Responses
X > −16


X > −8


X > 8


X > 16

Answer 1

To solve the inequality \( 22 - 2x < 38 \), we will isolate \( x \) step by step.

1. First, subtract 22 from both sides:
\[
22 - 2x - 22 < 38 - 22
\]
This simplifies to:
\[
-2x < 16
\]

2. Next, divide both sides by -2. Remember that when you divide by a negative number, you need to reverse the inequality sign:
\[
x > \frac{16}{-2}
\]
This simplifies to:
\[
x > -8
\]

Thus, the solution to the inequality is:
\[
x > -8
\]

The correct response is:
**X > -8**