Absolute Value Equations

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Problem 1: Simplify $\frac{\left|x-y\right|}{2}$ if x = -4 and y = 12

Type your final answer in the blank.

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Problem 2: Find $\left|4x\right|-\left|5y\right|-z$ if x = -2, y = 10 and z = -3

Solve Absolute Value Equation

​ Notes Example 1: | x+9|=14

​Set up two equations equal to +14 and -14
X + 9 = 14 x + 9 = -14
Then solve for x on each.
x + 9 = 14 and x + 9 = -14
-9 -9 -9 -9
x = 5 and x = -23 (answers)

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Problem 3: What is the biggest solution for the absolute value?

$\left|x+6\right|=13$

Multiple Select

Problem 4: What are the solutions for

$$\left|x-15\right|=26$$

• 11

• 41

• -41

• -11

Solve Absolute Value Equation

​Example 2: | 2x-4|=12

​Set up two equations equal to +12 and -12
2x - 4 = 12 and 2x - 4 = -12
Then solve for x on each.
2x - 4 = 12 and 2x - 4 = -12
+ 4 +4 + 4 +4
2x = 16 and 2x = - 8
2/2x = 16/2 and 2/2x = -8/2
x = 8 and x = -4 (answers)

Multiple Select

Problem 5: What are the solutions for

$$\left|4x-1\right|=11$$ ?

• 3

• -3

• -2.75

• -2.5

• 2.5

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Problem 6: What is the smallest solution of the absolute value equation?

$\left|5x+1\right|=46$

Solve Absolute Value Equation

Notes Example 3: |x +5|-8=11

move 8 first by adding it on both sides​
| x + 5 | - 8 = 11
+ 8 + 8
|x + 5| = 19

​Set up two equations:
x + 5 = 19 and x + 5 = -19
-5 -5 -5 -5
x = 14 and x = -24 (answers)

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Problem 7: What is the sum of the solutions for the absolute value equation:

$\left|x-7\right|+2=11$

Multiple Select

Problem 8: Which solutions are true for $$\left|x+2\right|-6=18$$ ?

• 20

• 22

• 26

• -26

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Problem 9: The solution x = 5 is a solution for the equation $\left|x-3\right|-8=-6$ .

true or false. Type true or false in the blank lower case only.

Solve Absolute Value Equation

Notes Example 4: 4|x - 1| + 2 = 12

​subtract 2 then divide by 4 first,
then make your
two equations.
4|x-1| + 2 = 12
-2 -2
4|x - 1| = 10
4/4|x-1| = 10/4
|x - 1| = 2.5

​Set up two equations 2.5 and -2.5
x - 1 = 2.5 and x - 1 = -2.5
+ 1 + 1 + 1 + 1
x = 3.5 and x = -1.5 (answers)

Multiple Select

Problem 10: Solve: $$6\left|x-2\right|+4=28$$

• x = 6

• x= -2

• x = 4

• x = -4