To find the interval for the first piece, find where the inside of the absolute value is non-negative.

Solve the inequality.

Subtract <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from both sides of the inequality.

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><mi>x</mi><mo>≥</mo><mo>-</mo><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><mi>x</mi><mo>≥</mo><mo>-</mo><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> . 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 <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> .

In the piece where <math><mstyle displaystyle="true"><mn>3</mn><mo>-</mo><mn>3</mn><mi>x</mi></mstyle></math> 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 <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from both sides of the inequality.

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><mi>x</mi><mo><</mo><mo>-</mo><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><mi>x</mi><mo><</mo><mo>-</mo><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> . 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 <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> .

In the piece where <math><mstyle displaystyle="true"><mn>3</mn><mo>-</mo><mn>3</mn><mi>x</mi></mstyle></math> is negative, remove the absolute value and multiply by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Write as a piecewise.

Simplify <math><mstyle displaystyle="true"><mn>2</mn><mrow><mo>(</mo><mn>3</mn><mo>-</mo><mn>3</mn><mi>x</mi><mo>)</mo></mrow><mo>-</mo><mn>2</mn><mo><</mo><mn>22</mn></mstyle></math> .

Simplify each term.

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mn>2</mn><mrow><mo>(</mo><mo>-</mo><mrow><mo>(</mo><mn>3</mn><mo>-</mo><mn>3</mn><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>-</mo><mn>2</mn><mo><</mo><mn>22</mn></mstyle></math> .

Simplify each term.

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> from <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>4</mn><mo><</mo><mn>22</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Move all terms not containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the right side of the inequality.

Subtract <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> from both sides of the inequality.

Subtract <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>22</mn></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn><mi>x</mi><mo><</mo><mn>18</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn><mi>x</mi><mo><</mo><mn>18</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> . 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 <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mn>18</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> .

Find the intersection of <math><mstyle displaystyle="true"><mi>x</mi><mo>></mo><mo>-</mo><mn>3</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>x</mi><mo>≤</mo><mn>1</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mn>6</mn><mi>x</mi><mo>-</mo><mn>8</mn><mo><</mo><mn>22</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Move all terms not containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the right side of the inequality.

Add <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> to both sides of the inequality.

Add <math><mstyle displaystyle="true"><mn>22</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mn>6</mn><mi>x</mi><mo><</mo><mn>30</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>6</mn><mi>x</mi><mo><</mo><mn>30</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Cancel the common factor.

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mn>30</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Find the intersection of <math><mstyle displaystyle="true"><mi>x</mi><mo><</mo><mn>5</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>x</mi><mo>></mo><mn>1</mn></mstyle></math> .

Find the union of the solutions.

The result can be shown in multiple forms.

Inequality Form:

Interval Notation:

Do you know how to Solve the Absolute Value Inequality for x 2|3-3x|-2<22? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

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

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

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

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

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

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

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

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

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