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9.4: Inequalities and Absolute Value

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9.4: Inequalities and Absolute Value

Pilar Alcazar

Period 1

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- Since there is a fraction with a denominator of 4, you need to multiply both sides of the equation by 4 or 4/1. Also, the absolute value means you need to do a positive and negative version of the equation.
3x+2/4≤ 5|3x+2/4 ≥ -5

x4/1 x4|x4x4

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2. Now, you need to subtract 2 from both sides of the equation because there is a 2 added onto the 3x. Add 2 to both sides of the second equation because the 2 is negative.

3x+2≤ 20| 3x+2≥ -20

-2-2|-2 -2

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3. Now you want to get the x all by itself. You need to divide both sides by 3 to isolate x. In the second equation, divide both sides by negative three and flip the sign from ≥ to ≤.

3x≤ 18| 3x≥ -22

÷3 ÷3|÷3÷3

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4. Since x is now isolated, you are finished with the equation.

x ≤ 6| x ≥ -22/3

Answer: {x|-22/3≤x≤6}

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1. Since this is an absolute value equation, you need to write it in a positive and negative form.

2b-4< -5 | 2b-4> 5

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2. Now you need to isolate the number that is multiplied onto b and b itself by either adding or subtracting.

2b-4< -5 | 2b-4> 5

+4+4|+4+4

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3. Now you need to isolate b by dividing by the number that is multiplied onto it.

2b<-1| 2b>9

÷2 ÷2| ÷2 ÷2

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- Now that b is by itself, you have your answer.
b<-1/2| b>9/2

Answer: {b|b<-1/2 or b>9/2}

If you go back and plug the answer in, you find out that these solutions do not validate. Therefore, there is no solution.

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