Example  1
Solve \(\left| 2x + 2\right| = 2 - x \) graphically. Verify the solutions using substitution.

Graph \(f(x) = \left|2x + 2\right| \) and \(g(x) = 2 - x\).


The points of intersection are \((–4, 6)\) and \((0, 2)\), so \(x = -4\) and \(x = 0\) are solutions to the equation. These can be verified using substitution.

Verify for \(x = -4\).

Left Side Right Side
\(\begin{array}{r}
 \left| {2x + 2} \right| \\
 \left| {2\left( { - 4} \right) + 2} \right| \\
 \left| { - 6} \right| \\
 6  \end{array}\)
 \(\begin{array}{l}
 2 - x \\
 2 - \left( { - 4} \right) \\
 6 \end{array}\)
  LS = RS

Verify for \(x = 0\).

Left Side Right Side
\(\begin{array}{r}
 \left| {2x + 2} \right| \\
 \left| {2\left( 0 \right) + 2} \right| \\
 \left| 2 \right| \\
 2 \end{array}\)
 \(\begin{array}{l}
 2 - x \\
 2 - 0 \\
 2 \end{array}\)
LS = RS