Solving Absolute Value Equations

By the end of this lesson you will be able to:Solve absolute value equations analytically.

GPS MM2A1c

Review of absolute value

• Absolute value is defined as the distance from zero. (Can distance be negative??)

For example:

rrr

yyy

555

333

What would be the answer to the following:

?8

?14

x

Solving Absolute Value Equations

• In order to solve absolute value equations, we must remember that xxandxx

So when we solve absolute value equations we need to split the equation up into a positive and negative expression. For example:

62 x

62x 62 x4x 8x

Find the positive solution.

Find the negative solution

Absolute value part of the equation needs to be by itself!!

Solving Absolute Value Equations

What about solving this one? 521 x

Much like solving quadratic equations, we need to isolate the variable part from the constants.

31

22

521

x

x

4

31

x

x2

31

x

x

Isolate the abs value!

2 7 6 12

2 7 18

7 9

x

x

x

Now you can split into two equations!

7 9

2

x

x

7 9

16

x

x

Solving Absolute Value Equations with Variables on Both Sides

284 xx

3

10x

103 x

284 xx

5

6x

65 x

)2(84 xx

284 xx

Decide whether the number is a solution to the equation.

2 5 9; 2x

So we take -2 and plug it in for x.

2( 2) 5 9 4 5 9

9 9 9 9

Decide whether the number is a solution to the equation.

5 1 11 0;4x

No; the two solutions are x=2 and x=-12/5

Practice Problems:

712 x 55 x

835 x 3 ( 2) 2 10x

4,3

5

11,1 6, 2

10,0

Classwork/Homework

• P. 30 (1-15) and p. 31 (1-9)