How do you solve equations involving absolute value?

Answer 1

Definition of Absolute Value: Absolute Value is the constant distance from zero; meaning that the distance from zero for any number, both positive and negative, is the same for each individual number.

Example: Find the absolute value of " l -123 l "

The distance from -123 from zero and the distance from 123 is the same; this goes for any number.

Absolute value of l -123 l is equal to 123.

*Note* Absolute Value is always Positive.

Now, onto the infamous equations involving absolute value.

Let's make up an equation.

l 2x + 2 l = 26

To find the value of X, you must always assume the existence of both positive and negative solutions; hence, it is called absolute value as explained above.

Set up two equations; one for positive, one for negative.

2x + 2 = 26 2x + 2 = -26

Solve individually for X.

2x + 2 = 26

Subtract 2 from each side.

2x = 26 - 2

2x = 24

Divide 2 on each side.

x = 12

Onto the other equation.

2x + 2 = -26

Similarly, subtract 2.

2x = -28

Divide by 2.

x = -14

The two solutions are x = 12 and x = -14 which can be denoted by:

X {12, -14}

*To Check for Extranneous Solutions; ALWAYS substitute the values back in to see if they are valid.*