Questions: Solve the compound inequalities: -8x + 0 > 8 or x + 2 < 2 Write the answer in interval notation.

Solution Steps

The first inequality is: \[ -8x + 0 > 8 \] Simplify the inequality: \[ -8x > 8 \] Divide both sides by \(-8\) (remember to reverse the inequality sign when dividing by a negative number): \[ x < -1 \]

The second inequality is: \[ x + 2 < 2 \] Subtract \(2\) from both sides: \[ x < 0 \]

The compound inequality uses "or," so the solution is the union of the two individual solutions: \[ x < -1 \quad \text{or} \quad x < 0 \] Since \(x < -1\) is already included in \(x < 0\), the solution simplifies to: \[ x < 0 \]

Final Answer