UNIT 4 , LESSON 5

Absolute Value Equations

Review of Absolute Value

http://www.brainpop.com/math/numbersandoperations/absolutevalue/preview.weml

The absolute-value of a number is that numbers distance from zero on a number line.

For example, |–5| = 5.

5 4 3 2 0 1 2 3 4 56 1 6

5 units

Both 5 and –5 are a distance of 5 units from 0, so both 5 and –5 have an absolute value of 5.

1. Isolate the absolute-value expression

2. Split the problem into two cases.

How to Solve Absolute Value Equations:

Solve the equation.

|x| – 3 = 4+ 3 +3

|x| = 7

x = 7

–x = 7

–1(–x) = –1(7)

x = –7

Solve |a| – 3 = 5 + 3 + 3

|a| = 8

a = 8 or a = –8

Example:

Solve the equation.

|x 2| = 8

+2 +2

x 2 = 8

x = 10

+2 +2

x = 6

x 2 = 8

Solve |3c – 6| = 9

3c – 6 = 9 3c – 6 = –9

+ 6 + 6

3c = 15 3

3

c = 5

Example:

+ 6 + 6

3c = –3 3

3

c = –1

|x + 7| = 8

x + 7 = 8

x + 7 = –8– 7 –7 – 7 – 7

x = 1 x = –15

3

3

Not all absolute-value equations have solutions.

If an equation states that an absolute-value is negative, there are no solutions.

CAREFUL!

Solve the equation.

2 |2x 5| = 72 2

|2x 5| = 5

Absolute values cannot be negative.

|2x 5| = 5

This equation has no solution.

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