# 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.
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
Solve the inequality.
Subtract from both sides of the inequality.
Divide each term in by and simplify.
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.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
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.
Subtract from both sides of the inequality.
Divide each term in by and simplify.
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.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Divide by .
In the piece where is negative, remove the absolute value and multiply by .
Write as a piecewise.
Simplify .
Simplify each term.
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Simplify .
Simplify each term.
Apply the distributive property.
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Solve when .
Solve for .
Move all terms not containing to the right side of the inequality.
Subtract from both sides of the inequality.
Subtract from .
Divide each term in by and simplify.
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.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Divide by .
Find the intersection of and .
Solve when .
Solve for .
Move all terms not containing to the right side of the inequality.
Add to both sides of the inequality.
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
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