Question

solve the compound inequality.
2x - 3 ≥ 3 or 3x - 1 ≤ -1
graph the solution on the number line.

Explanation:

Step1: Solve \(2x - 3\geq3\)

Add 3 to both sides: \(2x-3 + 3\geq3 + 3\), so \(2x\geq6\).
Divide both sides by 2: \(x\geq\frac{6}{2}\), so \(x\geq3\).

Step2: Solve \(3x - 1\leq - 1\)

Add 1 to both sides: \(3x-1 + 1\leq - 1+1\), so \(3x\leq0\).
Divide both sides by 3: \(x\leq\frac{0}{3}\), so \(x\leq0\).

Answer:

The solution of the compound inequality \(2x - 3\geq3\) or \(3x - 1\leq - 1\) is \(x\leq0\) or \(x\geq3\). On the number - line, we have a closed circle at \(x = 0\) and shade to the left (for \(x\leq0\)), and a closed circle at \(x = 3\) and shade to the right (for \(x\geq3\)).