Solve 2/5(x+1/2)div1/3(10-x)

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

Evaluate

$$-\frac{6x^{2}}{5}+\frac{57x}{5}+6$$

Solution Steps

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

$$\frac{\frac{2}{5}x+\frac{2}{5}\times \frac{1}{2}}{\frac{1}{3}}\left(10-x\right)$$

Multiply \frac{2}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2}{5}x+\frac{2\times 1}{5\times 2}}{\frac{1}{3}}\left(10-x\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{2}{5}x+\frac{1}{5}}{\frac{1}{3}}\left(10-x\right)$$

Divide \frac{2}{5}x+\frac{1}{5} by \frac{1}{3} by multiplying \frac{2}{5}x+\frac{1}{5} by the reciprocal of \frac{1}{3}.

$$\left(\frac{2}{5}x+\frac{1}{5}\right)\times 3\left(10-x\right)$$

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

$$\left(\frac{2}{5}x\times 3+\frac{1}{5}\times 3\right)\left(10-x\right)$$

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

$$\left(\frac{2\times 3}{5}x+\frac{1}{5}\times 3\right)\left(10-x\right)$$

Multiply 2 and 3 to get 6.

$$\left(\frac{6}{5}x+\frac{1}{5}\times 3\right)\left(10-x\right)$$

Multiply \frac{1}{5} and 3 to get \frac{3}{5}.

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

Apply the distributive property by multiplying each term of \frac{6}{5}x+\frac{3}{5} by each term of 10-x.

$$\frac{6}{5}x\times 10+\frac{6}{5}x\left(-1\right)x+\frac{3}{5}\times 10+\frac{3}{5}\left(-1\right)x$$

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

$$\frac{6}{5}x\times 10+\frac{6}{5}x^{2}\left(-1\right)+\frac{3}{5}\times 10+\frac{3}{5}\left(-1\right)x$$

Express \frac{6}{5}\times 10 as a single fraction.

$$\frac{6\times 10}{5}x+\frac{6}{5}x^{2}\left(-1\right)+\frac{3}{5}\times 10+\frac{3}{5}\left(-1\right)x$$

Multiply 6 and 10 to get 60.

$$\frac{60}{5}x+\frac{6}{5}x^{2}\left(-1\right)+\frac{3}{5}\times 10+\frac{3}{5}\left(-1\right)x$$

Divide 60 by 5 to get 12.

$$12x+\frac{6}{5}x^{2}\left(-1\right)+\frac{3}{5}\times 10+\frac{3}{5}\left(-1\right)x$$

Multiply \frac{6}{5} and -1 to get -\frac{6}{5}.

$$12x-\frac{6}{5}x^{2}+\frac{3}{5}\times 10+\frac{3}{5}\left(-1\right)x$$

Express \frac{3}{5}\times 10 as a single fraction.

$$12x-\frac{6}{5}x^{2}+\frac{3\times 10}{5}+\frac{3}{5}\left(-1\right)x$$

Multiply 3 and 10 to get 30.

$$12x-\frac{6}{5}x^{2}+\frac{30}{5}+\frac{3}{5}\left(-1\right)x$$

Divide 30 by 5 to get 6.

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

Multiply \frac{3}{5} and -1 to get -\frac{3}{5}.

$$12x-\frac{6}{5}x^{2}+6-\frac{3}{5}x$$

Combine 12x and -\frac{3}{5}x to get \frac{57}{5}x.

$$\frac{57}{5}x-\frac{6}{5}x^{2}+6$$

Expand

$$-\frac{6x^{2}}{5}+\frac{57x}{5}+6$$

Solution Steps

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

$$\frac{\frac{2}{5}x+\frac{2}{5}\times \frac{1}{2}}{\frac{1}{3}}\left(10-x\right)$$

Multiply \frac{2}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2}{5}x+\frac{2\times 1}{5\times 2}}{\frac{1}{3}}\left(10-x\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{2}{5}x+\frac{1}{5}}{\frac{1}{3}}\left(10-x\right)$$

Divide \frac{2}{5}x+\frac{1}{5} by \frac{1}{3} by multiplying \frac{2}{5}x+\frac{1}{5} by the reciprocal of \frac{1}{3}.

$$\left(\frac{2}{5}x+\frac{1}{5}\right)\times 3\left(10-x\right)$$

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

$$\left(\frac{2}{5}x\times 3+\frac{1}{5}\times 3\right)\left(10-x\right)$$

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

$$\left(\frac{2\times 3}{5}x+\frac{1}{5}\times 3\right)\left(10-x\right)$$

Multiply 2 and 3 to get 6.

$$\left(\frac{6}{5}x+\frac{1}{5}\times 3\right)\left(10-x\right)$$

Multiply \frac{1}{5} and 3 to get \frac{3}{5}.

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

Apply the distributive property by multiplying each term of \frac{6}{5}x+\frac{3}{5} by each term of 10-x.

$$\frac{6}{5}x\times 10+\frac{6}{5}x\left(-1\right)x+\frac{3}{5}\times 10+\frac{3}{5}\left(-1\right)x$$

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

$$\frac{6}{5}x\times 10+\frac{6}{5}x^{2}\left(-1\right)+\frac{3}{5}\times 10+\frac{3}{5}\left(-1\right)x$$

Express \frac{6}{5}\times 10 as a single fraction.

$$\frac{6\times 10}{5}x+\frac{6}{5}x^{2}\left(-1\right)+\frac{3}{5}\times 10+\frac{3}{5}\left(-1\right)x$$

Multiply 6 and 10 to get 60.

$$\frac{60}{5}x+\frac{6}{5}x^{2}\left(-1\right)+\frac{3}{5}\times 10+\frac{3}{5}\left(-1\right)x$$

Divide 60 by 5 to get 12.

$$12x+\frac{6}{5}x^{2}\left(-1\right)+\frac{3}{5}\times 10+\frac{3}{5}\left(-1\right)x$$

Multiply \frac{6}{5} and -1 to get -\frac{6}{5}.

$$12x-\frac{6}{5}x^{2}+\frac{3}{5}\times 10+\frac{3}{5}\left(-1\right)x$$

Express \frac{3}{5}\times 10 as a single fraction.

$$12x-\frac{6}{5}x^{2}+\frac{3\times 10}{5}+\frac{3}{5}\left(-1\right)x$$

Multiply 3 and 10 to get 30.

$$12x-\frac{6}{5}x^{2}+\frac{30}{5}+\frac{3}{5}\left(-1\right)x$$

Divide 30 by 5 to get 6.

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

Multiply \frac{3}{5} and -1 to get -\frac{3}{5}.

$$12x-\frac{6}{5}x^{2}+6-\frac{3}{5}x$$

Combine 12x and -\frac{3}{5}x to get \frac{57}{5}x.

$$\frac{57}{5}x-\frac{6}{5}x^{2}+6$$