Question

solve for all values of y in simplest form. |6 + 5y| = 18

Explanation:

Step1: Set up two equations

Since \(|a| = b\) implies \(a = b\) or \(a=-b\), for \(|6 + 5y|=18\), we have \(6 + 5y=18\) or \(6 + 5y=-18\).

Step2: Solve the first equation

Solve \(6 + 5y=18\). Subtract 6 from both sides: \(5y=18 - 6\), so \(5y = 12\). Then divide both sides by 5, we get \(y=\frac{12}{5}\).

Step3: Solve the second equation

Solve \(6+5y=-18\). Subtract 6 from both sides: \(5y=-18 - 6\), so \(5y=-24\). Then divide both sides by 5, we get \(y =-\frac{24}{5}\).

Answer:

\(y=\frac{12}{5},y =-\frac{24}{5}\)