Solve.

Question

|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: \[ (-10, 4) \]