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Ratio Scale Time Math Interior and Exterior Angles Ratio Scale Fraction Exponents Sample Standard Deviation Area of an EllipseAn absolute value inequality is slightly different to an absolute value equation, examples of which
can be seen on the __ absolute value
equations__ page.

When we had an equality, something like

solving it meant finding what

The solutions were exact numbers.

In this case the solutions are

Solutions to absolute value inequalities examples would instead look something like

Solving this means finding what

The solutions are any

So we are looking for an interval of values with absolute value inequalities.

Solving absolute inequality such as this requires writing up the absolute value inequality as a

Here this is:

Which on a number line graph would be presented like so.

The open circle at each end indicate that **4** and **-4** themselves will NOT be among the
values of solutions.

Solving

Solve

This example, is asking to find a value or values of

So thinking in terms of distance, considering zero as a starting point.

If the size of the distance from

So the initial form in this example, can be written as a double inequality, then solved as such.

This is the solution, an interval of different * x* values
between

But not

This can also be written as

Solve

Absolute value inequalities examples such as this one, follow the same approach as example (1.1), with the initial set up being a double inequality.

Though this time the inequality is less than OR equal to

This is also an interval, that can also be written as * x* ∈

Square brackets mean that unlike in example (1.1),

In a number line graph this is illustrated as:

The closed circles at the end points indicate that **-4** and **1** are included as
solutions, as the original inequality was less than or equal to.

Solve

The set up to solving absolute value inequalities examples that involve the greater than symbol, is a
little bit different to the less than symbol.

If we think about **| x |** >

It's asking what

We can observe these values on a number line graph.

The ** x** values that are a distance of more than

So what to do to solve a greater than example, is to set up a compound inequality with "or", then proceed.

Solve

This compound inequality is the solution.

** x** values less than