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

In the piece where <math><mstyle displaystyle="true"><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.

In the piece where <math><mstyle displaystyle="true"><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.

Find the intersection of <math><mstyle displaystyle="true"><mi>x</mi><mo>></mo><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>x</mi><mo>≥</mo><mn>0</mn></mstyle></math> .

Multiply each term in <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi><mo>></mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math>

Multiply each term in <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi><mo>></mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

Multiply <math><mstyle displaystyle="true"><mrow><mo>(</mo><mo>-</mo><mi>x</mi><mo>)</mo></mrow><mo>⋅</mo><mo>-</mo><mn>1</mn></mstyle></math> .

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

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

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

Find the intersection of <math><mstyle displaystyle="true"><mi>x</mi><mo><</mo><mo>-</mo><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>x</mi><mo><</mo><mn>0</mn></mstyle></math> .

Find the union of the solutions.

Convert the inequality to interval notation.

Do you know how to Convert to Interval Notation |x|>1? 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.