simplifying and solving 0123456-2-3-4-5-6 1 medina

Simplifying and Solving

0 1 2 3 4 5 6-1-2-3-4-5-6

1Medina

Absolute Value– The absolute value of a number is the distance from zero

Since distance can not be negative, the absolute value of a number is always positive.

However, that does not mean that an absolute value equation will only have positives value for the variable.

Absolute value equation have two solutions because you can move in two different directions on the number line.

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3

3

Absolute value is 3

Ask yourself, how many steps do you take to 3? 

What is the absolute value of ?

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8

8Absolute value is 8

Ask yourself, how many steps do you take to -8? 

What is the absolute value of ?

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9

9

_

Ask yourself, how many steps do you take to 9? 

What is the absolute value of ?

9But have we used the negative sign yet? 

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7

7

_

Ask yourself, how many steps do you take to -7? 

What is the absolute value of ?

7But have we used the negative sign yet? 

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Step 1– simplify the expression inside the absolute value sign

Step 2– Take the absolute value

Step 3– Simplify the expression

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8 7

15

15

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1 7

6

6

1 7

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4 6

10

10

_

_

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8 3

5

5

_

_

11Medina

Absolute Value– The absolute value of a number is the distance from zero

Absolute value equation have two solutions because you can move in two different directions on the number line.

1. Isolate the absolute value sign2. Separate the equation into the two possible

equations3. Solve for the variable4. Check solutions

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13Medina

The absolute value of x is the distance from zero. If | x | = 4 

0 1 2 3 4 5 6-1-2-3-4-5-6

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Therefore x = 4 or -4 because they are both 4 steps away from zero.  

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The absolute value of x is the distance from zero. If | x | = -5 

0 1 2 3 4 5 6-1-2-3-4-5-6

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therefore its No Solution

Wait!!!!Think about it

Can we take -5 steps?

No, distance is always positive

1. Isolate the absolute value sign

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3 5x

2. Separate the equation into the two possible equations

3. Solve for the variable4. Check solutions

38 5

55

2 3 5

5 5

1. Isolate the absolute value sign

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4 7 8x 2. Separate the equation into the two possible equations

3. Solve for the variable4. Check solutions

3 74 8

1 87

5 74 8

1 87

4 1x

71 8 1 7 8

1. Isolate the absolute value sign

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2 6 8x 2. Separate the equation into the two possible equations

3. Solve for the variable4. Check solutions

2 610 8

2 4 8

2 62 8

2 4 8

6 4x

2 84 2 4 8

2 2

6 4x 6 4x 6 6 6 6

10x 2x

1. Isolate the absolute value sign

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2 6 8 2x 2. Separate the equation into the two possible equations3. Solve for the variable4. Check solutions

83 262

6 8 2

89 262

6 8 2

2 6 6x

2 3 8 2 2 3 8 2

2 2

6 3x 6 3x 6 6 6 6

3x 9x

8 8

6 3x

2 3 28 2 3 28

1. Isolate the absolute value sign

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2 3 5 8x 2. Separate the equation into the two possible equations

3 5 4x

2 2

3 5 4x !!!!Wait

x No solution

Think about it…

Can we take -4 steps?No, distance is always positive