simplifying and solving 0123456-2-3-4-5-6 1 medina
TRANSCRIPT
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
_
_
10Medina
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