Question

solve the compound inequality. 4x - 4 < - 20 or 2x + 2 ≥ 4. graph the solution on the number line.

Explanation:

Step1: Solve the first - inequality

Solve \(4x - 4\lt - 20\). Add 4 to both sides: \(4x-4 + 4\lt-20 + 4\), which simplifies to \(4x\lt - 16\). Then divide both sides by 4: \(x\lt - 4\).

Step2: Solve the second - inequality

Solve \(2x+2\geq4\). Subtract 2 from both sides: \(2x + 2-2\geq4 - 2\), which simplifies to \(2x\geq2\). Then divide both sides by 2: \(x\geq1\).

Step3: Graph the solutions

For \(x\lt - 4\), we use an open - circle at \(x=-4\) and shade to the left. For \(x\geq1\), we use a closed - circle at \(x = 1\) and shade to the right.

Answer:

The solution of the compound inequality is \(x\lt - 4\) or \(x\geq1\). On the number line, there is an open circle at \(-4\) with shading to the left and a closed circle at \(1\) with shading to the right.