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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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solving equations with absolute values

Today’s Lesson

Solving Equations with Absolute Values

slide2

Warm- Up Activity

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

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

slide3

The answers are

|4| = 4

|-8| = 8

|1| = 1

|0| = 0

|-6| = 6

slide4

Whole-Class Skills Lesson

Today you will be solving absolute value equations.

slide5
Absolute value equations are used to find maximum and minimum values of certain situations.
slide6
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.

slide9

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

|x-3| = 2

there are two solutions.

slide10
When an absolute value equation has two solutions,

|X + 4| = 3

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

slide11

: 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

slide12
Solve this equation.

|x + 4| = -2

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

slide13

|x – 5| = 0

Rewrite this as an equation

x – 5 = 0 and then solve.

The solution to this equation is x = 5.

slide14

|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.)

slide15
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

slide17
Solve this equation.

|x + 2| + 4 = 2

There is no solution to this equation.

slide18
Solve this equation.

|x – 8| – 3 = -3

The solution to this equation is x = 8.

slide19
Solve this equation.

|x + 2| – 5 = 12

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