Question

solve and graph the following inequality: $-8x - 7 < 8$ or $-4 > 1 + x$

Explanation:

Step1: Solve the first inequality

Solve \(-8x - 7 < 8\).
Add \(7\) to both sides: \(-8x<8 + 7\), so \(-8x<15\).
Divide both sides by \(-8\) (and reverse the inequality sign): \(x>-\frac{15}{8}\).

Step2: Solve the second inequality

Solve \(-4>1 + x\).
Subtract \(1\) from both sides: \(-4-1>x\), so \(x < - 5\).

Answer:

The solution of the compound inequality \(-8x - 7 < 8\) or \(-4>1 + x\) is \(x>-\frac{15}{8}\) or \(x < - 5\).
To graph:

• For \(x>-\frac{15}{8}=-1.875\), draw an open circle at \(-1.875\) and shade to the right.
• For \(x < - 5\), draw an open circle at \(-5\) and shade to the left.