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write the answer in interval notation

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|12-5x|<22  solve and check the inequality.
asked Mar 11, 2014 in ALGEBRA 2 by johnkelly Apprentice

1 Answer

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The inequality is |12 - 5x | < 22.

Write |12 - 5x | < 22 as (12 - 5x ) < 22 and (12 - 5x ) > - 22

Case 1 : (12 - 5x ) is positive.

(12 - 5x ) < 22

Subtract 12 from each side.

- 5x < 22 - 12

- 5x < 10

Divide each side by negative 5 and flip the symbol.

x > - 10/5

x > - 2.

Case 2 : (12 - 5x ) is negative.

- (12 - 5x ) < 22

Multiply each side by negative 1 and flip the symbol.

(12 - 5x ) > - 22

Subtract 12 from each side.

- 5x > -22 - 12

- 5x > - 34

Divide each side by negative 5 and flip the symbol.

x < 34/5.

Solution set is {x | - 2 < x < 34/5}.

answered Mar 24, 2014 by dozey Mentor

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