Question

solve for all values of b in simplest form.
10 = \left| \frac{b}{5} \
ight|

Explanation:

Step1: Recall absolute value definition

The absolute value equation \(|x| = a\) (where \(a\geq0\)) has solutions \(x = a\) or \(x=-a\). Here, \(x=\frac{b}{5}\) and \(a = 10\), so we have two cases: \(\frac{b}{5}=10\) or \(\frac{b}{5}=-10\).

Step2: Solve for \(b\) in each case

• For \(\frac{b}{5}=10\): Multiply both sides by 5. \(b=10\times5 = 50\).
• For \(\frac{b}{5}=-10\): Multiply both sides by 5. \(b=-10\times5=-50\).

Answer:

\(b = 50\) or \(b=-50\)