Question

Solve each equation. Then graph the solution set.

$2\left|h\right|-3=8$

Short answer

The equation $2\left|h\right|-3=8$has solution set as$h=5.5,-5.5$ 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 2h−3=8.

Simplify the expression for h.

$\begin{array}{c}2h-3+3=8+3\\ 2h=11\\ \frac{2h}{2}=\frac{11}{2}\\ h=5.5\end{array}$

Step-3. Formulate case 2 when 2−h−3=8.

Simplify the expression for h.

$\begin{array}{c}2\left(-h\right)-3+3=8+3\\ -2h=11\\ \frac{-2h}{\left(-2\right)}=\frac{11}{\left(-2\right)}\\ h=-5.5\end{array}$

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

From case 1 and case 2, $h=5.5,-5.5$. Plot these values on the number line.