Solve.

Question

|x+2|=7

Answer 1

To solve the equation \( |x + 2| = 7 \), we need to consider the two cases that arise from the definition of absolute value.

Case 1:

\( x + 2 = 7 \)

Subtracting 2 from both sides, we get: \[ x = 7 - 2 = 5 \]

Case 2:

\( x + 2 = -7 \)

Again, subtracting 2 from both sides, we have: \[ x = -7 - 2 = -9 \]

Solutions

The solutions to the equation \( |x + 2| = 7 \) are: \[ x = 5 \quad \text{and} \quad x = -9 \]

So the final answer is: \[ \boxed{5 \text{ and } -9} \]