Solve the Absolute Value Inequality for x 2|3-3x|-2<22

Solve the Absolute Value Inequality for x 2|3-3x|-2<22
Write as a piecewise.
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To find the interval for the first piece, find where the inside of the absolute value is non-negative.
Solve the inequality.
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Subtract from both sides of the inequality.
Divide each term in by and simplify.
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Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify the right side.
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Divide by .
In the piece where is non-negative, remove the absolute value.
To find the interval for the second piece, find where the inside of the absolute value is negative.
Solve the inequality.
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Subtract from both sides of the inequality.
Divide each term in by and simplify.
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Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify the right side.
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Divide by .
In the piece where is negative, remove the absolute value and multiply by .
Write as a piecewise.
Simplify .
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Simplify each term.
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Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Simplify .
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Simplify each term.
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Apply the distributive property.
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Solve when .
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Solve for .
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Move all terms not containing to the right side of the inequality.
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Subtract from both sides of the inequality.
Subtract from .
Divide each term in by and simplify.
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Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify the right side.
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Divide by .
Find the intersection of and .
Solve when .
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Solve for .
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Move all terms not containing to the right side of the inequality.
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Add to both sides of the inequality.
Add and .
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify the right side.
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Divide by .
Find the intersection of and .
Find the union of the solutions.
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
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Name

Name seven hundred ninety million seven hundred forty-nine thousand seventy-three

Interesting facts

  • 790749073 has 4 divisors, whose sum is 792120100
  • The reverse of 790749073 is 370947097
  • Previous prime number is 577

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 46
  • Digital Root 1

Name

Name six hundred eight million seven hundred sixteen thousand seven hundred thirty

Interesting facts

  • 608716730 has 16 divisors, whose sum is 1098800424
  • The reverse of 608716730 is 037617806
  • Previous prime number is 353

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 38
  • Digital Root 2

Name

Name two billion eighty-five million five hundred thirty-six thousand four hundred seventy-four

Interesting facts

  • 2085536474 has 16 divisors, whose sum is 3576279168
  • The reverse of 2085536474 is 4746355802
  • Previous prime number is 3623

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 44
  • Digital Root 8