1.8
Watch the video and then solve the problem given below.
Click here to watch the video.
Solve the inequality.

Question

1.8 Watch the video and then solve the problem given below. Click here to watch the video. Solve the inequality. $$ |2 x+7|<7 $$

UpStudy AI · Accepted Answer

1. Start with the inequality:
$$
|2x+7|<7
$$

2. Rewrite the absolute value inequality as a compound inequality:
$$
-7 < 2x+7 < 7
$$

3. Subtract $$7$$ from all parts of the inequality:
$$
-7 - 7 < 2x+7-7 < 7-7
$$
$$
-14 < 2x < 0
$$

4. Divide every part by $$2$$ (since $$2$$ is positive, the inequality signs remain unchanged):
$$
\frac{-14}{2} < x < \frac{0}{2}
$$
$$
-7 < x < 0
$$

Thus, the solution to the inequality is:
$$
-7 < x < 0
$$
The solution to the inequality $$ |2x + 7| < 7 $$ is $$ -7 < x < 0 $$.

1.8
Watch the video and then solve the problem given below.
Click here to watch the video.
Solve the inequality.

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