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Special Solutions in Absolute Value Inequalities

Objective: Solve absolute value inequalitiesIdentify special solutions for absolute value inequalities

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Which number line shows "NO SOLUTION"?

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Which solution set is "ALL REAL NUMBERS"?

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Possible or Impossible?

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Absolute values do not yield a negative value.

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Absolute values do not yield a negative value.

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Absolute values do not yield a negative value.

When you see an equation like |x| = -4, you know that the equation has NO SOLUTION. Similarly, an inequality like |x| < -4, you know that the inequality has no solution. The absolute value of x cannot be less than a negative value.

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Solve & Graph the inequality

|8 - 2x| > -8

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Solve & Graph the inequality

|3x-6| < 0

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An absolute value greater than a negative value?|x+1| > -8 Duhh. Of course it has to be greater than a negative! ALL REAL NUMBERS!

An absolute value less than a negative value?|x+1| < -8 No way! It can't be negative! NO SOLUTION!

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Next

steps

-4|x+1|>4

Isolate the absolute value.
Rewrite with AND/OR.
Solve each case.
Graph the solution set.
Write the final inequality.

Next

steps

-4|x+1|<4

Isolate the absolute value.
Rewrite with AND/OR.
Solve each case.
Graph the solution set.
Write the final inequality.

Next

Which inequality has a solution set of ALL REAL numbers?

Next

Remember to complete your CFU in edio!

Special Solutions in Absolute Value Equations

You should be able to: Solve absolute value inequalities Identify special solutions for absolute value inequalities