Question

1. solve for x: |-4 + 5x| = 16

Explanation:

Step1: Set up two equations

Since \(|a| = b\) implies \(a = b\) or \(a=-b\), we have \(-4 + 5x=16\) or \(-4 + 5x=-16\).

Step2: Solve the first equation

For \(-4 + 5x=16\), add 4 to both sides: \(5x=16 + 4\), so \(5x=20\). Then divide both sides by 5, we get \(x = 4\).

Step3: Solve the second equation

For \(-4+5x=-16\), add 4 to both sides: \(5x=-16 + 4\), so \(5x=-12\). Then divide both sides by 5, we get \(x=-\frac{12}{5}\).

Answer:

\(x = 4\) or \(x=-\frac{12}{5}\)