Questions: Solve: x+6>5

Solution Steps

To solve the inequality \( |x+6| > 5 \), we need to consider the definition of absolute value. The inequality \( |x+6| > 5 \) means that \( x+6 \) is either greater than 5 or less than -5. Therefore, we split the inequality into two separate inequalities: \( x+6 > 5 \) and \( x+6 < -5 \). We then solve each inequality separately.

To solve \( |x+6| > 5 \), we split it into two separate inequalities:

1. \( x + 6 > 5 \)
2. \( x + 6 < -5 \)

Solve the first inequality: \[ x + 6 > 5 \] Subtract 6 from both sides: \[ x > -1 \]

Solve the second inequality: \[ x + 6 < -5 \] Subtract 6 from both sides: \[ x < -11 \]

The solution to the inequality \( |x+6| > 5 \) is the union of the solutions to the two inequalities: \[ x > -1 \quad \text{or} \quad x < -11 \]

Final Answer