Question

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

Piecewise-Defined Functions
ANSWERED
asked 2020-11-08
Write an absolute value equation that has solutions of -3 and 11.

Answers (1)

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.
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