Questions: Inequality 8-x>5

Solution Steps

To solve the inequality \( |8 - x| > 5 \), we need to consider the definition of absolute value. The inequality \( |A| > B \) translates to two separate inequalities: \( A > B \) or \( A < -B \). Applying this to our problem, we get two cases: \( 8 - x > 5 \) or \( 8 - x < -5 \). We then solve these inequalities separately to find the solution set.

1. Solve the inequality \( 8 - x > 5 \).
2. Solve the inequality \( 8 - x < -5 \).
3. Combine the solutions from both inequalities.

The given inequality is \( |8 - x| > 5 \). This is an absolute value inequality, which can be split into two separate inequalities.

The absolute value inequality \( |8 - x| > 5 \) can be split into two cases:

1. \( 8 - x > 5 \)
2. \( 8 - x < -5 \)

\[ 8 - x > 5 \] Subtract 8 from both sides: \[ -x > -3 \] Multiply both sides by -1 (and reverse the inequality sign): \[ x < 3 \]

\[ 8 - x < -5 \] Subtract 8 from both sides: \[ -x < -13 \] Multiply both sides by -1 (and reverse the inequality sign): \[ x > 13 \]

The solutions from both cases are: \[ x < 3 \quad \text{or} \quad x > 13 \]

Final Answer