Solve 2x(3/5x-1/2)+4x(3/5x-1/2)-(frac{3}{5}x-frac{1}{2})

$$2x( \frac{ 3 }{ 5 } x- \frac{ 1 }{ 2 } )+4x( \frac{ 3 }{ 5 } x- \frac{ 1 }{ 2 } )-( \frac{ 3 }{ 5 } x- \frac{ 1 }{ 2 } )$$

Evaluate

$$\frac{18x^{2}}{5}-\frac{18x}{5}+\frac{1}{2}$$

Solution Steps

Use the distributive property to multiply 2x by \frac{3}{5}x-\frac{1}{2}.

$$2x\times \frac{3}{5}x+2x\left(-\frac{1}{2}\right)+4x\left(\frac{3}{5}x-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Multiply x and x to get x^{2}.

$$2x^{2}\times \frac{3}{5}+2x\left(-\frac{1}{2}\right)+4x\left(\frac{3}{5}x-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Express 2\times \frac{3}{5} as a single fraction.

$$\frac{2\times 3}{5}x^{2}+2x\left(-\frac{1}{2}\right)+4x\left(\frac{3}{5}x-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Multiply 2 and 3 to get 6.

$$\frac{6}{5}x^{2}+2x\left(-\frac{1}{2}\right)+4x\left(\frac{3}{5}x-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Cancel out 2 and 2.

$$\frac{6}{5}x^{2}-x+4x\left(\frac{3}{5}x-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Use the distributive property to multiply 4x by \frac{3}{5}x-\frac{1}{2}.

$$\frac{6}{5}x^{2}-x+4x\times \frac{3}{5}x+4x\left(-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Multiply x and x to get x^{2}.

$$\frac{6}{5}x^{2}-x+4x^{2}\times \frac{3}{5}+4x\left(-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Express 4\times \frac{3}{5} as a single fraction.

$$\frac{6}{5}x^{2}-x+\frac{4\times 3}{5}x^{2}+4x\left(-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Multiply 4 and 3 to get 12.

$$\frac{6}{5}x^{2}-x+\frac{12}{5}x^{2}+4x\left(-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Express 4\left(-\frac{1}{2}\right) as a single fraction.

$$\frac{6}{5}x^{2}-x+\frac{12}{5}x^{2}+\frac{4\left(-1\right)}{2}x-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Multiply 4 and -1 to get -4.

$$\frac{6}{5}x^{2}-x+\frac{12}{5}x^{2}+\frac{-4}{2}x-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Divide -4 by 2 to get -2.

$$\frac{6}{5}x^{2}-x+\frac{12}{5}x^{2}-2x-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Combine \frac{6}{5}x^{2} and \frac{12}{5}x^{2} to get \frac{18}{5}x^{2}.

$$\frac{18}{5}x^{2}-x-2x-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Combine -x and -2x to get -3x.

$$\frac{18}{5}x^{2}-3x-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

To find the opposite of \frac{3}{5}x-\frac{1}{2}, find the opposite of each term.

$$\frac{18}{5}x^{2}-3x-\frac{3}{5}x-\left(-\frac{1}{2}\right)$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\frac{18}{5}x^{2}-3x-\frac{3}{5}x+\frac{1}{2}$$

Combine -3x and -\frac{3}{5}x to get -\frac{18}{5}x.

$$\frac{18}{5}x^{2}-\frac{18}{5}x+\frac{1}{2}$$

Expand

$$\frac{18x^{2}}{5}-\frac{18x}{5}+\frac{1}{2}$$

Solution Steps

Use the distributive property to multiply 2x by \frac{3}{5}x-\frac{1}{2}.

$$2x\times \frac{3}{5}x+2x\left(-\frac{1}{2}\right)+4x\left(\frac{3}{5}x-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Multiply x and x to get x^{2}.

$$2x^{2}\times \frac{3}{5}+2x\left(-\frac{1}{2}\right)+4x\left(\frac{3}{5}x-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Express 2\times \frac{3}{5} as a single fraction.

$$\frac{2\times 3}{5}x^{2}+2x\left(-\frac{1}{2}\right)+4x\left(\frac{3}{5}x-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Multiply 2 and 3 to get 6.

$$\frac{6}{5}x^{2}+2x\left(-\frac{1}{2}\right)+4x\left(\frac{3}{5}x-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Cancel out 2 and 2.

$$\frac{6}{5}x^{2}-x+4x\left(\frac{3}{5}x-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Use the distributive property to multiply 4x by \frac{3}{5}x-\frac{1}{2}.

$$\frac{6}{5}x^{2}-x+4x\times \frac{3}{5}x+4x\left(-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Multiply x and x to get x^{2}.

$$\frac{6}{5}x^{2}-x+4x^{2}\times \frac{3}{5}+4x\left(-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Express 4\times \frac{3}{5} as a single fraction.

$$\frac{6}{5}x^{2}-x+\frac{4\times 3}{5}x^{2}+4x\left(-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Multiply 4 and 3 to get 12.

$$\frac{6}{5}x^{2}-x+\frac{12}{5}x^{2}+4x\left(-\frac{1}{2}\right)-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Express 4\left(-\frac{1}{2}\right) as a single fraction.

$$\frac{6}{5}x^{2}-x+\frac{12}{5}x^{2}+\frac{4\left(-1\right)}{2}x-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Multiply 4 and -1 to get -4.

$$\frac{6}{5}x^{2}-x+\frac{12}{5}x^{2}+\frac{-4}{2}x-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Divide -4 by 2 to get -2.

$$\frac{6}{5}x^{2}-x+\frac{12}{5}x^{2}-2x-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Combine \frac{6}{5}x^{2} and \frac{12}{5}x^{2} to get \frac{18}{5}x^{2}.

$$\frac{18}{5}x^{2}-x-2x-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

Combine -x and -2x to get -3x.

$$\frac{18}{5}x^{2}-3x-\left(\frac{3}{5}x-\frac{1}{2}\right)$$

To find the opposite of \frac{3}{5}x-\frac{1}{2}, find the opposite of each term.

$$\frac{18}{5}x^{2}-3x-\frac{3}{5}x-\left(-\frac{1}{2}\right)$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\frac{18}{5}x^{2}-3x-\frac{3}{5}x+\frac{1}{2}$$

Combine -3x and -\frac{3}{5}x to get -\frac{18}{5}x.

$$\frac{18}{5}x^{2}-\frac{18}{5}x+\frac{1}{2}$$