Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>x</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> from both sides of the inequality.

To write <math><mstyle displaystyle="true"><mfrac><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

To write <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>2</mn><mi>x</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> , by multiplying each by an appropriate factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

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"><mfrac><mrow><mn>2</mn><mi>x</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

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

Combine the numerators over the common denominator.

Simplify each term.

Simplify the numerator.

Factor <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mi>x</mi><mo>⋅</mo><mn>3</mn><mo>-</mo><mn>2</mn><mi>x</mi><mo>⋅</mo><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mi>x</mi><mo>⋅</mo><mn>3</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn><mi>x</mi><mo>⋅</mo><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mi>x</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mo>+</mo><mi>x</mi><mrow><mo>(</mo><mo>-</mo><mn>2</mn><mo>⋅</mo><mn>2</mn><mo>)</mo></mrow></mstyle></math> .

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

Subtract <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Move <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Move the negative in front of the fraction.

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

To write <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

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

Subtract <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Move the negative in front of the fraction.

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>x</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo><</mo><mo>-</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></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.

Simplify the left side.

Dividing two negative values results in a positive value.

Divide <math><mstyle displaystyle="true"><mfrac><mrow><mi>x</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Dividing two negative values results in a positive value.

Divide <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply both sides 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.

Rewrite the expression.

Simplify the right side.

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>⋅</mo><mn>6</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

The result can be shown in multiple forms.

Inequality Form:

Interval Notation:

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