Question

# Write an absolute value equation that has solutions of -3 and 11.

Piecewise-Defined Functions
Write an absolute value equation that has solutions of -3 and 11.

2020-11-09
Step 1
The absolute value equation has solution of -3 is,
$$\displaystyle{\left|{x}+{3}\right|}={0}$$
Now the solution is.
$$\displaystyle{\left|{x}+{3}\right|}={0}$$
$$\displaystyle-{\left({x}+{3}\right)}={0}\ {\quad\text{and}\quad}\ {x}+{3}={0}$$
$$\displaystyle-{x}-{3}={0}\ {\quad\text{and}\quad}\ {x}=-{3}$$
$$\displaystyle-{x}={3}\ {\quad\text{and}\quad}\ {x}=-{3}$$
$$\displaystyle{x}=-{3}\ {\quad\text{and}\quad}\ {x}=-{3}$$
In both case the solution is -3
Step 2
The absolute value equation has solution of 11 is,
$$\displaystyle{\left|{x}-{11}\right|}={0}$$
Now the solution is.
$$\displaystyle{\left|{x}-{11}\right|}={0}$$
$$\displaystyle-{\left({x}-{11}\right)}={0}\ {\quad\text{and}\quad}\ {x}-{11}={0}$$
$$\displaystyle-{x}+{11}={0}\ {\quad\text{and}\quad}\ {x}={11}$$
$$\displaystyle-{x}=-{11}\ {\quad\text{and}\quad}\ {x}={11}$$
$$\displaystyle{x}={11}\ {\quad\text{and}\quad}{x}={11}$$
In both case the solution is 11.