SOLVING ABSOLUTE VALUE EQUATIONS

SOLVING ABSOLUTE VALUE EQUATIONS

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Absolute Value is the distance from zero.

**ALWAYS POSITIVE**

• Distance is NEVER negative (for example: when you travel, you always travel in positive miles... you NEVER say " I went negative 5 miles back home.)

Multiple Choice

What is the reason that absolute value is always written as a positive?

• Absolute value is talking about numbers so it must be positive.
• Absolute value does not always have to be positive.
• Absolute value is like a clock it has only positive numbers.
• Absolute value is talking about distance, distance is always measured by positive numbers.

Multiple Choice

What is the absolute value of |-26|.

• 26

• -26

• 0

• -20

Multiple Choice

What is the absolute value of |6|.

• 6

• -6

• 0

• undefined

Multiple Choice

What is the absolute value of |0|.

• 6

• -6

• 0

• undefined

EXAMPLE #1: 

• Evaluate the following if n= - 15/2 and p=3.

•  $\left|2n-p\right|+4$  

• Watch video for full explanation.

• NO Decimals; only fraction answers

EXAMPLE #2: 

• Evaluate the following if n= - 15/2 and p=3.

•  $-\left|p^3\right|-n$  

• Watch video for full explanation.

• NO Decimals; only fraction answers

SOLVING AN ABSOLUTE VALUE EQUATION

• STEP 1: Get absolute value on one side of equal sign by itself.

• STEP 2: Split into 2 equations (one for positive answer and one for negative)

• STEP 3: Solve each of the equations.

• STEP 4: Write answer in set notation.

• (next slide/video walks you through these steps)

Multiple Choice

∣ 2x + 9 ∣ = 15

• {3}

• { -6,3}

• { -12,3}

• { -12,6}

Multiple Choice

−2|−2r − 4| = -12

• {5,1}

• {-5,1}

• {-5}

• No Solution

Multiple Choice

3| −8x| + 8 = 80

• {-7/3, 7/3}
• {-3,3}
• {11/3,-11/3}
• No Solution

Get Absolute Value by itself and then watch video.

•  $\left|3x-2\right|+8=1$  

Multiple Choice

 |−2n| + 10 = −50

• {30, -30}
• {20,-20}
• {-5,5}
• No Solution

Fill in the Blank

solve for z.

|3z|+1=10

Fill in the Blank

Solve for p

-6|-2p - 7| = -18