Question

solve the compound inequality.
2x - 3 ≥ 9 or 4x - 1 < -25
graph the solution on the number line.

Explanation:

Step1: Solve \(2x - 3\geq9\)

Add 3 to both sides: \(2x - 3 + 3\geq9 + 3\)
Simplify: \(2x\geq12\)
Divide both sides by 2: \(\frac{2x}{2}\geq\frac{12}{2}\)
Simplify: \(x\geq6\)

Step2: Solve \(4x - 1\lt - 25\)

Add 1 to both sides: \(4x - 1 + 1\lt - 25 + 1\)
Simplify: \(4x\lt - 24\)
Divide both sides by 4: \(\frac{4x}{4}\lt\frac{-24}{4}\)
Simplify: \(x\lt - 6\)

Answer:

The solution to the compound inequality \(2x - 3\geq9\) or \(4x - 1\lt - 25\) is \(x\lt - 6\) or \(x\geq6\).

To graph this on the number line:

• For \(x\lt - 6\), draw an open circle at \(-6\) and shade to the left.
• For \(x\geq6\), draw a closed circle at \(6\) and shade to the right.