Question

Solve.
|x+3|<7

Answer 1

To solve the inequality \( |x+3| < 7 \), we can break it down into two separate inequalities:

1. \( x + 3 < 7 \)
2. \( x + 3 > -7 \)

Now, we will solve each inequality step by step.

**For the first inequality:**
\[
x + 3 < 7
\]
Subtract 3 from both sides:
\[
x < 4
\]

**For the second inequality:**
\[
x + 3 > -7
\]
Subtract 3 from both sides:
\[
x > -10
\]

Now we combine the results from both inequalities. The solution to the original inequality \( |x+3| < 7 \) is:
\[
-10 < x < 4
\]

In interval notation, this is written as:
\[
(-10, 4)
\]

So the final answer is:
\[
(-10, 4)
\]