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.

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.