High School Math Solutions – Absolute Value Inequalities Calculator

In the last post we covered absolute value equations (click here for the previous post) and the need for understanding the absolute value property. Here, solid understanding of the inequality property is required as well, which makes absolute value inequalities more challenging (click here for a quick review of inequalities).

Let’s start with simple absolute value inequalities:

• For inequalities of the form |f(x)| < a the solution is always –a < f(x) < a
• For inequalities of the form |f(x)| > a the solution is always f(x) < -a or f(x) > a

Either way, this leaves us with two simple inequalities to solve.

Here's how it works (click here):

Here's another example (click here):

Solving inequalities involving variables is very similar to solving absolute value equations with variables. You should first find the positive and negative ranges of the absolute values.  Write the simple inequalities for the different ranges, solve and validate the solutions are within the range.

Here's how it works (click here):

If you’re up for a challenge try this one    

Or click here for the solution…


Until next time,
Michal

High School Math Solutions – Absolute Value Equation Calculator

Solving absolute value equations is somewhat tricky; it requires understanding of the absolute value property.

In short, to solve simple absolute value equations first isolate the absolute value on one side of the equation, numbers on the other side.  Write two simple equations without absolute values like this:  |f(x)|=a  =>  f(x)=a  or  f(x)=-a

Finally, solve the two simple equations.  (click here for a quick review of simple equations)

Here's how it works (click here):

Solving equations involving multiple absolute values or variables requires some more attention.

Here you should first find the positive and negative ranges of the absolute values.  Write the simple equations for the different ranges, solve and validate the solutions are within the range.

Here's how it works (click here):

Until next time,
Michal