Solve 4x(3/2x-5)-(3/2x-5)

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

Evaluate

$$6x^{2}-\frac{43x}{2}+5$$

Solution Steps

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

$$4x\times \frac{3}{2}x-20x-\left(\frac{3}{2}x-5\right)$$

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

$$4x^{2}\times \frac{3}{2}-20x-\left(\frac{3}{2}x-5\right)$$

Express 4\times \frac{3}{2} as a single fraction.

$$\frac{4\times 3}{2}x^{2}-20x-\left(\frac{3}{2}x-5\right)$$

Multiply 4 and 3 to get 12.

$$\frac{12}{2}x^{2}-20x-\left(\frac{3}{2}x-5\right)$$

Divide 12 by 2 to get 6.

$$6x^{2}-20x-\left(\frac{3}{2}x-5\right)$$

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

$$6x^{2}-20x-\frac{3}{2}x-\left(-5\right)$$

The opposite of -5 is 5.

$$6x^{2}-20x-\frac{3}{2}x+5$$

Combine -20x and -\frac{3}{2}x to get -\frac{43}{2}x.

$$6x^{2}-\frac{43}{2}x+5$$

Expand

$$6x^{2}-\frac{43x}{2}+5$$

Solution Steps

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

$$4x\times \frac{3}{2}x-20x-\left(\frac{3}{2}x-5\right)$$

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

$$4x^{2}\times \frac{3}{2}-20x-\left(\frac{3}{2}x-5\right)$$

Express 4\times \frac{3}{2} as a single fraction.

$$\frac{4\times 3}{2}x^{2}-20x-\left(\frac{3}{2}x-5\right)$$

Multiply 4 and 3 to get 12.

$$\frac{12}{2}x^{2}-20x-\left(\frac{3}{2}x-5\right)$$

Divide 12 by 2 to get 6.

$$6x^{2}-20x-\left(\frac{3}{2}x-5\right)$$

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

$$6x^{2}-20x-\frac{3}{2}x-\left(-5\right)$$

The opposite of -5 is 5.

$$6x^{2}-20x-\frac{3}{2}x+5$$

Combine -20x and -\frac{3}{2}x to get -\frac{43}{2}x.

$$6x^{2}-\frac{43}{2}x+5$$