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Absolute Value Inequalities

Absolute value is nothing but the values without considering its sign. Here we are going to solve the absolute values for inequalities. If we solve the absolute value inequalities we will get two values. Normally absolute value of |a| = $\pm$ a.

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Absolute Values Inequalities Examples

Example 1: Find the absolute values of the inequalities: |x - 2| $\geq$ 10

Solution:

Given inequality is |x - 2| $\geq$ 10

To find the absolute value for the inequality is

(x - 2) $\geq$ 10     ............. (1) and
- (x - 2) $\geq$ 10      ..............(2)

Equation 1:

(x - 2) $\geq$ 10 ...........(1)

Add + 2 on both sides

x - 2 + 2 $\geq$ 10 + 2

x  $\geq$ 12

Equation 2:

-(x - 2) $\geq$ 10

- x + 2 $\geq$ 10

Add - 2 on both sides.

- x + 2 - 2 $\geq$ 10 - 2

- x $\geq$ 8

Divide by - 1 on each side

x $\leq$ -8

Answer: x lies between -8 $\geq$ x $\geq$ 12

Example 2: Find the absolute values of the inequalities. |x - 5| $\geq$ 2

Solution:

Given inequality is |x - 5| $\geq$ 2

To find the absolute value for the inequality is

(x - 5) $\geq$ 2        .................(1) and

- (x - 5) $\geq$ 2      .................. (2)

Equation 1:

(x - 5) $\geq$ 2  .................(1)

Add + 5 on both sides

x - 5 + 5 $\geq$ 2 + 5

x $\geq$ 7

Equation 2:

-(x - 5) $\geq$ 2

- x + 5 $\geq$ 2

-x + 5 - 5 $\geq$ 2 - 5

-x $\geq$ -3

Divide by -1.

x $\leq$ 1

Answer: x lies between 7 $\geq$ x $\geq$ 1

 More topics in  Absolute Value Inequalities Solving Absolute Value Inequalities Graphing Absolute Value Inequalities
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