Enter an equation or problem
Camera input is not recognized!

Solution - Absolute value equations

Exact form: m=0,0
m=0 , 0

Other Ways to Solve

Absolute value equations

Step-by-step explanation

1. Rewrite the equation with one absolute value terms on each side

|m||m|=0

Add |m| to both sides of the equation:

|m||m|+|m|=|m|

Simplify the arithmetic

|m|=|m|

2. Rewrite the equation without absolute value bars

Use the rules:
|x|=|y|x=±y and |x|=|y|±x=y
to write all four options of the equation
|m|=|m|
without the absolute value bars:

|x|=|y||m|=|m|
x=+y(m)=(m)
x=y(m)=((m))
+x=y(m)=(m)
x=y(m)=(m)

When simplified, equations x=+y and +x=y are the same and equations x=y and x=y are the same, so we end up with only 2 equations:

|x|=|y||m|=|m|
x=+y , +x=y(m)=(m)
x=y , x=y(m)=((m))

3. Solve the two equations for m

2 additional steps

m=m

Subtract from both sides:

m-m=m-m

Simplify the arithmetic:

0=m-m

Simplify the arithmetic:

0=0

3 additional steps

m=-m

Add to both sides:

m+m=-m+m

Simplify the arithmetic:

2m=-m+m

Simplify the arithmetic:

2m=0

Divide both sides by the coefficient:

m=0

4. List the solutions

m=0,0
(2 solution(s))

5. Graph

Each line represents the function of one side of the equation:
y=|m|
y=|m|
The equation is true where the two lines cross.

Why learn this

We encounter absolute values almost daily. For example: If you walk 3 miles to school, do you also walk minus 3 miles when you go back home? The answer is no because distances use absolute value. The absolute value of the distance between home and school is 3 miles, there or back.
In short, absolute values help us deal with concepts like distance, ranges of possible values, and deviation from a set value.