Question

3 ) solve and graph the compound inequality -4 > 3x - 7 > 8

Explanation:

Step1: Split the compound inequality

Split \(-4>3x - 7>8\) into two inequalities: \(-4>3x - 7\) and \(3x - 7>8\).

Step2: Solve \(-4>3x - 7\)

Add \(7\) to both sides: \(-4 + 7>3x-7 + 7\), which simplifies to \(3>3x\).
Divide both sides by \(3\): \(\frac{3}{3}>\frac{3x}{3}\), so \(1>x\) or \(x < 1\).

Step3: Solve \(3x - 7>8\)

Add \(7\) to both sides: \(3x-7 + 7>8 + 7\), which simplifies to \(3x>15\).
Divide both sides by \(3\): \(\frac{3x}{3}>\frac{15}{3}\), so \(x>5\).

Answer:

The solution is \(x < 1\) or \(x>5\). On the number - line, for \(x < 1\), we have an open circle at \(x = 1\) and an arrow pointing to the left. For \(x>5\), we have an open circle at \(x = 5\) and an arrow pointing to the right.