Subtract <math><mstyle displaystyle="true"><mn>5</mn><mi>x</mi></mstyle></math> from both sides of the inequality.

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>9</mn><mi>y</mi><mo>≥</mo><mn>8</mn><mo>-</mo><mn>5</mn><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>9</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>9</mn><mi>y</mi><mo>≥</mo><mn>8</mn><mo>-</mo><mn>5</mn><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>9</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>9</mn></mstyle></math> .

Cancel the common factor.

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

Dividing two negative values results in a positive value.

Subtract <math><mstyle displaystyle="true"><mn>7</mn><mi>x</mi></mstyle></math> from both sides of the inequality.

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mi>y</mi><mo><</mo><mn>10</mn><mo>-</mo><mn>7</mn><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mi>y</mi><mo><</mo><mn>10</mn><mo>-</mo><mn>7</mn><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>4</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>4</mn></mstyle></math> .

Cancel the common factor.

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

Simplify the right side.

Simplify each term.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> and <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Dividing two negative values results in a positive value.

Find the intersection of <math><mstyle displaystyle="true"><mi>y</mi><mo>≤</mo><mo>-</mo><mfrac><mrow><mn>8</mn></mrow><mrow><mn>9</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>5</mn><mi>x</mi></mrow><mrow><mn>9</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mi>y</mi><mo>></mo><mo>-</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>7</mn><mi>x</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

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