If any individual factor on the left side of the equation is equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , the entire expression will be equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>1</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to both sides of the equation.

Set <math><mstyle displaystyle="true"><mn>3</mn><mi>x</mi><mo>-</mo><mn>4</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mn>3</mn><mi>x</mi><mo>-</mo><mn>4</mn><mo>=</mo><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> to both sides of the equation.

Divide each term in <math><mstyle displaystyle="true"><mn>3</mn><mi>x</mi><mo>=</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>3</mn><mi>x</mi><mo>=</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Simplify the left side.

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

The final solution is all the values that make <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>4</mn><mo>)</mo></mrow><mo>≥</mo><mn>0</mn></mstyle></math> true.

Use each root to create test intervals.

Test a value on the interval <math><mstyle displaystyle="true"><mi>x</mi><mo><</mo><mn>1</mn></mstyle></math> to see if it makes the inequality true.

Choose a value on the interval <math><mstyle displaystyle="true"><mi>x</mi><mo><</mo><mn>1</mn></mstyle></math> and see if this value makes the original inequality true.

Replace <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> in the original inequality.

The left side <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> is greater than the right side <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , which means that the given statement is always true.

True

True

Test a value on the interval <math><mstyle displaystyle="true"><mn>1</mn><mo><</mo><mi>x</mi><mo><</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> to see if it makes the inequality true.

Choose a value on the interval <math><mstyle displaystyle="true"><mn>1</mn><mo><</mo><mi>x</mi><mo><</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> and see if this value makes the original inequality true.

Replace <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>1.17</mn></mstyle></math> in the original inequality.

The left side <math><mstyle displaystyle="true"><mo>-</mo><mn>0.0833</mn></mstyle></math> is less than the right side <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , which means that the given statement is false.

False

False

Test a value on the interval <math><mstyle displaystyle="true"><mi>x</mi><mo>></mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> to see if it makes the inequality true.

Choose a value on the interval <math><mstyle displaystyle="true"><mi>x</mi><mo>></mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> and see if this value makes the original inequality true.

Replace <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> in the original inequality.

The left side <math><mstyle displaystyle="true"><mn>24</mn></mstyle></math> is greater than the right side <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , which means that the given statement is always true.

True

True

Compare the intervals to determine which ones satisfy the original inequality.

The solution consists of all of the true intervals.

The result can be shown in multiple forms.

Inequality Form:

Interval Notation:

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