How To Solve Absolute Value Equation

What is the $x$ that makes $|x|=2$ ? The answer is really simple $x=2$ or $x=-2$ . In general if $a>0$ (this is important). The equation $|x|=a$ always has to solutions, namely $x=\pm a$ . So the strategy of solving equation with absolute value is to bring the absolute value to the left hand side and the rest on the right hand side and then use the property that $|x|=a$ has solutions $x=\pm a$ . Here is an example:

Solve $|2x+1|+5=7$ .

Rewrite the equation as $|2x+1|=2$ . Now think of the terms inside the absolute value as one single entity. Then using the property mentioned above this entity must be equal to 2 or -2, mathematically $2x+1=2$ or $2x+1=-2$ and then you can solve each of these equation.

The video playlist below will give you more examples on how to solve equation with absolute value.