Solving Equations with Absolute Values

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# Solving Equations with Absolute Values - PowerPoint PPT Presentation

Today’s Lesson. Solving Equations with Absolute Values. Warm- Up Activity. We will warm up today by solving for the absolute values of |4|; |-8|; |1|; |0|; |-6|. The answers are |4| = 4 |-8| = 8 |1| = 1 |0| = 0 |-6| = 6. Whole-Class Skills Lesson.

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Presentation Transcript

Today’s Lesson

Solving Equations with Absolute Values

Warm- Up Activity

We will warm up today by solving for the absolute values of

|4|; |-8|; |1|; |0|; |-6|

|4| = 4

|-8| = 8

|1| = 1

|0| = 0

|-6| = 6

Whole-Class Skills Lesson

Today you will be solving absolute value equations.

Absolute value equations are used to find maximum and minimum values of certain situations.
If an absolute value equation is equal to a negative number,

|x +3| = -2

then there is no solution since a distance cannot be negative.

### If an absolute value equation is equal to zero, |x+5| = 0 there is one solution.

If an absolute value equation is equal to a positive rational number greater than 0,

|x-3| = 2

there are two solutions.

When an absolute value equation has two solutions,

|X + 4| = 3

the absolute value equation needs to be re-written as two equations

: the first is equal to a positive number, and the second is equal to a negative number.

|X + 4| = 3 becomes,

X + 4 = 3 and X + 4 = -3

Solve this equation.

|x + 4| = -2

This equation has no solution since the equation is equal to a negative number.

|x – 5| = 0

Rewrite this as an equation

x – 5 = 0 and then solve.

The solution to this equation is x = 5.

|x + 6| = 14

Rewrite this as two equations

x + 6 = 14 and x + 6 = -14 and then solve each equation.

Answers: x = 8; x = -20

(The two solutions are 8 or -20; these are the minimum and maximum values.)

The length of a sleeve on a t-shirt is 18 centimeters and the sleeves can be altered by 2.75 centimeters to be longer or shorter, what are the possible lengths?

15.25 cm or 20.75 cm

Solve this equation.

|x + 2| + 4 = 2

There is no solution to this equation.

Solve this equation.

|x – 8| – 3 = -3

The solution to this equation is x = 8.

Solve this equation.

|x + 2| – 5 = 12

There are two solutions for this equation: x =15 or x = -19.