Enter an equation or problem
Camera input is not recognized!

Solution - Absolute value equations

Exact form: a=0,0
a=0 , 0

Other Ways to Solve

Absolute value equations

Step-by-step explanation

1. 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
|5a|=|4a|
without the absolute value bars:

|x|=|y||5a|=|4a|
x=+y(5a)=(4a)
x=y(5a)=(4a)
+x=y(5a)=(4a)
x=y(5a)=(4a)

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||5a|=|4a|
x=+y , +x=y(5a)=(4a)
x=y , x=y(5a)=(4a)

2. Solve the two equations for a

2 additional steps

5a=4a

Subtract from both sides:

(5a)-4a=(4a)-4a

Simplify the arithmetic:

a=(4a)-4a

Simplify the arithmetic:

a=0

11 additional steps

5a=4a

Divide both sides by :

(5a)5=(-4a)5

Simplify the fraction:

a=(-4a)5

Add to both sides:

a+45·a=((-4a)5)+45a

Group the coefficients:

(1+45)a=((-4a)5)+45a

Convert the integer into a fraction:

(55+45)a=((-4a)5)+45a

Combine the fractions:

(5+4)5·a=((-4a)5)+45a

Combine the numerators:

95·a=((-4a)5)+45a

Combine the fractions:

95·a=(-4+4)5a

Combine the numerators:

95·a=05a

Reduce the zero numerator:

95a=0a

Simplify the arithmetic:

95a=0

Divide both sides by the coefficient:

a=0

3. List the solutions

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

4. Graph

Each line represents the function of one side of the equation:
y=|5a|
y=|4a|
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.