Question

Solve each equation. Then graph the solution set.

$\left|-2y+6\right|=6$

Short answer

The equation $\left|-2y+6\right|=6$has solution set as $y=0$and $y=6$and the graph of the solution set is:

Step-by-step solution

Step-1. Define absolute value equation.

For any real numbers a and b, if $\left|a\right|=b$and $b\ge 0$, then $a=b$or $a=-b$.

Step-2. Formulate case 1 when −2y+6=6.

Simplify the expression for y.

$$\begin{gathered} -2y+6-6=6-6 \\ -2y=0 \\ \frac{-2y}{-2}=\frac{0}{-2} \\ y=0 \end{gathered}$$

Step-3. Formulate case 2 when −2y+6=−6.

Simplify the expression for y.

$$\begin{gathered} -2y+6-6=-6-6 \\ -2y=-12 \\ \frac{-2y}{-2}=\frac{-12}{-2} \\ y=6 \end{gathered}$$

Step-4. Plot the graph of the solution set.

From case 1 and case 2, $y=0,6$. Plot these values on the number line.