Rewrite the equation as <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn><mo>+</mo><mn>2</mn><mi>x</mi></mrow><mrow><mn>0.5</mn><mo>-</mo><mi>x</mi></mrow></mfrac><mo>=</mo><mn>3.5</mn></mstyle></math> .

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

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

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

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn><mo>+</mo><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>0.5</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>0.5</mn><mo>-</mo><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>0.5</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>0.5</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>0.5</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>0.5</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>0.5</mn><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mn>0.5</mn><mrow><mo>(</mo><mo>-</mo><mn>2</mn><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Separate fractions.

Divide <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0.5</mn></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mo>+</mo><mi>x</mi></mrow><mrow><mn>1</mn><mo>-</mo><mn>2</mn><mi>x</mi></mrow></mfrac></mstyle></math> .

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

Remove parentheses.

The LCM of one and any expression is the expression.

Multiply each term in <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>-</mo><mn>2</mn><mi>x</mi></mrow></mfrac><mo>=</mo><mn>3.5</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn><mo>-</mo><mn>2</mn><mi>x</mi></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>1</mn><mo>-</mo><mn>2</mn><mi>x</mi></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Apply the distributive property.

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

Simplify the right side.

Apply the distributive property.

Multiply.

Multiply <math><mstyle displaystyle="true"><mn>3.5</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3.5</mn></mstyle></math> .

Move all terms containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the left side of the equation.

Add <math><mstyle displaystyle="true"><mn>7</mn><mi>x</mi></mstyle></math> to both sides of the equation.

Add <math><mstyle displaystyle="true"><mn>4</mn><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>7</mn><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 equation.

Subtract <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>3.5</mn></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mn>11</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>4.5</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>11</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>11</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>4.5</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>11</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>11</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>4.5</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>11</mn></mstyle></math> .

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