Solve 5/2(3x-4/7)-5(4/3x-2)

$$\frac { 5 } { 2 } ( 3 x - \frac { 4 } { 7 } ) - 5 ( \frac { 4 } { 3 } x - 2 )$$

Evaluate

$$\frac{5x}{6}+\frac{60}{7}$$

Solution Steps

Use the distributive property to multiply \frac{5}{2} by 3x-\frac{4}{7}.

$$\frac{5}{2}\times 3x+\frac{5}{2}\left(-\frac{4}{7}\right)-5\left(\frac{4}{3}x-2\right)$$

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

$$\frac{5\times 3}{2}x+\frac{5}{2}\left(-\frac{4}{7}\right)-5\left(\frac{4}{3}x-2\right)$$

Multiply 5 and 3 to get 15.

$$\frac{15}{2}x+\frac{5}{2}\left(-\frac{4}{7}\right)-5\left(\frac{4}{3}x-2\right)$$

Multiply \frac{5}{2} times -\frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15}{2}x+\frac{5\left(-4\right)}{2\times 7}-5\left(\frac{4}{3}x-2\right)$$

Do the multiplications in the fraction \frac{5\left(-4\right)}{2\times 7}.

$$\frac{15}{2}x+\frac{-20}{14}-5\left(\frac{4}{3}x-2\right)$$

Reduce the fraction \frac{-20}{14} to lowest terms by extracting and canceling out 2.

$$\frac{15}{2}x-\frac{10}{7}-5\left(\frac{4}{3}x-2\right)$$

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

$$\frac{15}{2}x-\frac{10}{7}-5\times \frac{4}{3}x+10$$

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

$$\frac{15}{2}x-\frac{10}{7}+\frac{-5\times 4}{3}x+10$$

Multiply -5 and 4 to get -20.

$$\frac{15}{2}x-\frac{10}{7}+\frac{-20}{3}x+10$$

Fraction \frac{-20}{3} can be rewritten as -\frac{20}{3} by extracting the negative sign.

$$\frac{15}{2}x-\frac{10}{7}-\frac{20}{3}x+10$$

Combine \frac{15}{2}x and -\frac{20}{3}x to get \frac{5}{6}x.

$$\frac{5}{6}x-\frac{10}{7}+10$$

Convert 10 to fraction \frac{70}{7}.

$$\frac{5}{6}x-\frac{10}{7}+\frac{70}{7}$$

Since -\frac{10}{7} and \frac{70}{7} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}x+\frac{-10+70}{7}$$

Add -10 and 70 to get 60.

$$\frac{5}{6}x+\frac{60}{7}$$

Expand

$$\frac{5x}{6}+\frac{60}{7}$$

Solution Steps

Use the distributive property to multiply \frac{5}{2} by 3x-\frac{4}{7}.

$$\frac{5}{2}\times 3x+\frac{5}{2}\left(-\frac{4}{7}\right)-5\left(\frac{4}{3}x-2\right)$$

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

$$\frac{5\times 3}{2}x+\frac{5}{2}\left(-\frac{4}{7}\right)-5\left(\frac{4}{3}x-2\right)$$

Multiply 5 and 3 to get 15.

$$\frac{15}{2}x+\frac{5}{2}\left(-\frac{4}{7}\right)-5\left(\frac{4}{3}x-2\right)$$

Multiply \frac{5}{2} times -\frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15}{2}x+\frac{5\left(-4\right)}{2\times 7}-5\left(\frac{4}{3}x-2\right)$$

Do the multiplications in the fraction \frac{5\left(-4\right)}{2\times 7}.

$$\frac{15}{2}x+\frac{-20}{14}-5\left(\frac{4}{3}x-2\right)$$

Reduce the fraction \frac{-20}{14} to lowest terms by extracting and canceling out 2.

$$\frac{15}{2}x-\frac{10}{7}-5\left(\frac{4}{3}x-2\right)$$

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

$$\frac{15}{2}x-\frac{10}{7}-5\times \frac{4}{3}x+10$$

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

$$\frac{15}{2}x-\frac{10}{7}+\frac{-5\times 4}{3}x+10$$

Multiply -5 and 4 to get -20.

$$\frac{15}{2}x-\frac{10}{7}+\frac{-20}{3}x+10$$

Fraction \frac{-20}{3} can be rewritten as -\frac{20}{3} by extracting the negative sign.

$$\frac{15}{2}x-\frac{10}{7}-\frac{20}{3}x+10$$

Combine \frac{15}{2}x and -\frac{20}{3}x to get \frac{5}{6}x.

$$\frac{5}{6}x-\frac{10}{7}+10$$

Convert 10 to fraction \frac{70}{7}.

$$\frac{5}{6}x-\frac{10}{7}+\frac{70}{7}$$

Since -\frac{10}{7} and \frac{70}{7} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}x+\frac{-10+70}{7}$$

Add -10 and 70 to get 60.

$$\frac{5}{6}x+\frac{60}{7}$$