Question

solve each equation. then graph the solution set 1. |n - 3| = 5

Explanation:

Step1: Consider two - case for absolute - value

If \(|a| = b\) (\(b\geq0\)), then \(a = b\) or \(a=-b\). So for \(|n - 3|=5\), we have \(n−3 = 5\) or \(n−3=-5\).

Step2: Solve the first equation

Solve \(n−3 = 5\). Add 3 to both sides of the equation: \(n=5 + 3\), so \(n = 8\).

Step3: Solve the second equation

Solve \(n−3=-5\). Add 3 to both sides of the equation: \(n=-5 + 3\), so \(n=-2\).

Answer:

The solution set is \(\{-2,8\}\). To graph the solution set on a number - line, mark the points \(-2\) and \(8\) with closed circles (since the values are included in the solution set).