Solve 3(2x-1)-4(3x+2)+2/5(10x+15/2)

$$3 ( 2 x - 1 ) - 4 ( 3 x + 2 ) + \frac { 2 } { 5 } ( 10 x + \frac { 15 } { 2 } )$$

Evaluate

$$-2x-8$$

Solution Steps

Use the distributive property to multiply 3 by 2x-1.

$$6x-3-4\left(3x+2\right)+\frac{2}{5}\left(10x+\frac{15}{2}\right)$$

Use the distributive property to multiply -4 by 3x+2.

$$6x-3-12x-8+\frac{2}{5}\left(10x+\frac{15}{2}\right)$$

Combine 6x and -12x to get -6x.

$$-6x-3-8+\frac{2}{5}\left(10x+\frac{15}{2}\right)$$

Subtract 8 from -3 to get -11.

$$-6x-11+\frac{2}{5}\left(10x+\frac{15}{2}\right)$$

Use the distributive property to multiply \frac{2}{5} by 10x+\frac{15}{2}.

$$-6x-11+\frac{2}{5}\times 10x+\frac{2}{5}\times \frac{15}{2}$$

Express \frac{2}{5}\times 10 as a single fraction.

$$-6x-11+\frac{2\times 10}{5}x+\frac{2}{5}\times \frac{15}{2}$$

Multiply 2 and 10 to get 20.

$$-6x-11+\frac{20}{5}x+\frac{2}{5}\times \frac{15}{2}$$

Divide 20 by 5 to get 4.

$$-6x-11+4x+\frac{2}{5}\times \frac{15}{2}$$

Multiply \frac{2}{5} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$-6x-11+4x+\frac{2\times 15}{5\times 2}$$

Cancel out 2 in both numerator and denominator.

$$-6x-11+4x+\frac{15}{5}$$

Divide 15 by 5 to get 3.

$$-6x-11+4x+3$$

Combine -6x and 4x to get -2x.

$$-2x-11+3$$

Add -11 and 3 to get -8.

$$-2x-8$$

Expand

$$-2x-8$$

Solution Steps

Use the distributive property to multiply 3 by 2x-1.

$$6x-3-4\left(3x+2\right)+\frac{2}{5}\left(10x+\frac{15}{2}\right)$$

Use the distributive property to multiply -4 by 3x+2.

$$6x-3-12x-8+\frac{2}{5}\left(10x+\frac{15}{2}\right)$$

Combine 6x and -12x to get -6x.

$$-6x-3-8+\frac{2}{5}\left(10x+\frac{15}{2}\right)$$

Subtract 8 from -3 to get -11.

$$-6x-11+\frac{2}{5}\left(10x+\frac{15}{2}\right)$$

Use the distributive property to multiply \frac{2}{5} by 10x+\frac{15}{2}.

$$-6x-11+\frac{2}{5}\times 10x+\frac{2}{5}\times \frac{15}{2}$$

Express \frac{2}{5}\times 10 as a single fraction.

$$-6x-11+\frac{2\times 10}{5}x+\frac{2}{5}\times \frac{15}{2}$$

Multiply 2 and 10 to get 20.

$$-6x-11+\frac{20}{5}x+\frac{2}{5}\times \frac{15}{2}$$

Divide 20 by 5 to get 4.

$$-6x-11+4x+\frac{2}{5}\times \frac{15}{2}$$

Multiply \frac{2}{5} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$-6x-11+4x+\frac{2\times 15}{5\times 2}$$

Cancel out 2 in both numerator and denominator.

$$-6x-11+4x+\frac{15}{5}$$

Divide 15 by 5 to get 3.

$$-6x-11+4x+3$$

Combine -6x and 4x to get -2x.

$$-2x-11+3$$

Add -11 and 3 to get -8.

$$-2x-8$$