Solve for x -|3+3x|-2>-11

Solve for x -|3+3x|-2>-11
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 .
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 .
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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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 . 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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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 .
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 one billion eight hundred thirty-seven million two hundred seventy-two thousand seventy-four

Interesting facts

  • 1837272074 has 16 divisors, whose sum is 3008481696
  • The reverse of 1837272074 is 4702727381
  • Previous prime number is 11

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 41
  • Digital Root 5

Name

Name one billion seven million eighty-six thousand seventy-seven

Interesting facts

  • 1007086077 has 16 divisors, whose sum is 1128783600
  • The reverse of 1007086077 is 7706807001
  • Previous prime number is 809

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 36
  • Digital Root 9

Name

Name one billion one hundred ninety million five hundred nineteen thousand twenty

Interesting facts

  • 1190519020 has 64 divisors, whose sum is 3334763520
  • The reverse of 1190519020 is 0209150911
  • Previous prime number is 373

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 28
  • Digital Root 1