Solve 5/2(6x-7)+4/3(2+9x)

$$\frac { 5 } { 2 } ( 6 x - 7 ) + \frac { 4 } { 3 } ( 2 + 9 x )$$

Evaluate

$$27x-\frac{89}{6}$$

Solution Steps

Use the distributive property to multiply \frac{5}{2} by 6x-7.

$$\frac{5}{2}\times 6x+\frac{5}{2}\left(-7\right)+\frac{4}{3}\left(2+9x\right)$$

Express \frac{5}{2}\times 6 as a single fraction.

$$\frac{5\times 6}{2}x+\frac{5}{2}\left(-7\right)+\frac{4}{3}\left(2+9x\right)$$

Multiply 5 and 6 to get 30.

$$\frac{30}{2}x+\frac{5}{2}\left(-7\right)+\frac{4}{3}\left(2+9x\right)$$

Divide 30 by 2 to get 15.

$$15x+\frac{5}{2}\left(-7\right)+\frac{4}{3}\left(2+9x\right)$$

Express \frac{5}{2}\left(-7\right) as a single fraction.

$$15x+\frac{5\left(-7\right)}{2}+\frac{4}{3}\left(2+9x\right)$$

Multiply 5 and -7 to get -35.

$$15x+\frac{-35}{2}+\frac{4}{3}\left(2+9x\right)$$

Fraction \frac{-35}{2} can be rewritten as -\frac{35}{2} by extracting the negative sign.

$$15x-\frac{35}{2}+\frac{4}{3}\left(2+9x\right)$$

Use the distributive property to multiply \frac{4}{3} by 2+9x.

$$15x-\frac{35}{2}+\frac{4}{3}\times 2+\frac{4}{3}\times 9x$$

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

$$15x-\frac{35}{2}+\frac{4\times 2}{3}+\frac{4}{3}\times 9x$$

Multiply 4 and 2 to get 8.

$$15x-\frac{35}{2}+\frac{8}{3}+\frac{4}{3}\times 9x$$

Express \frac{4}{3}\times 9 as a single fraction.

$$15x-\frac{35}{2}+\frac{8}{3}+\frac{4\times 9}{3}x$$

Multiply 4 and 9 to get 36.

$$15x-\frac{35}{2}+\frac{8}{3}+\frac{36}{3}x$$

Divide 36 by 3 to get 12.

$$15x-\frac{35}{2}+\frac{8}{3}+12x$$

Least common multiple of 2 and 3 is 6. Convert -\frac{35}{2} and \frac{8}{3} to fractions with denominator 6.

$$15x-\frac{105}{6}+\frac{16}{6}+12x$$

Since -\frac{105}{6} and \frac{16}{6} have the same denominator, add them by adding their numerators.

$$15x+\frac{-105+16}{6}+12x$$

Add -105 and 16 to get -89.

$$15x-\frac{89}{6}+12x$$

Combine 15x and 12x to get 27x.

$$27x-\frac{89}{6}$$

Expand

$$27x-\frac{89}{6}$$

Solution Steps

Use the distributive property to multiply \frac{5}{2} by 6x-7.

$$\frac{5}{2}\times 6x+\frac{5}{2}\left(-7\right)+\frac{4}{3}\left(2+9x\right)$$

Express \frac{5}{2}\times 6 as a single fraction.

$$\frac{5\times 6}{2}x+\frac{5}{2}\left(-7\right)+\frac{4}{3}\left(2+9x\right)$$

Multiply 5 and 6 to get 30.

$$\frac{30}{2}x+\frac{5}{2}\left(-7\right)+\frac{4}{3}\left(2+9x\right)$$

Divide 30 by 2 to get 15.

$$15x+\frac{5}{2}\left(-7\right)+\frac{4}{3}\left(2+9x\right)$$

Express \frac{5}{2}\left(-7\right) as a single fraction.

$$15x+\frac{5\left(-7\right)}{2}+\frac{4}{3}\left(2+9x\right)$$

Multiply 5 and -7 to get -35.

$$15x+\frac{-35}{2}+\frac{4}{3}\left(2+9x\right)$$

Fraction \frac{-35}{2} can be rewritten as -\frac{35}{2} by extracting the negative sign.

$$15x-\frac{35}{2}+\frac{4}{3}\left(2+9x\right)$$

Use the distributive property to multiply \frac{4}{3} by 2+9x.

$$15x-\frac{35}{2}+\frac{4}{3}\times 2+\frac{4}{3}\times 9x$$

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

$$15x-\frac{35}{2}+\frac{4\times 2}{3}+\frac{4}{3}\times 9x$$

Multiply 4 and 2 to get 8.

$$15x-\frac{35}{2}+\frac{8}{3}+\frac{4}{3}\times 9x$$

Express \frac{4}{3}\times 9 as a single fraction.

$$15x-\frac{35}{2}+\frac{8}{3}+\frac{4\times 9}{3}x$$

Multiply 4 and 9 to get 36.

$$15x-\frac{35}{2}+\frac{8}{3}+\frac{36}{3}x$$

Divide 36 by 3 to get 12.

$$15x-\frac{35}{2}+\frac{8}{3}+12x$$

Least common multiple of 2 and 3 is 6. Convert -\frac{35}{2} and \frac{8}{3} to fractions with denominator 6.

$$15x-\frac{105}{6}+\frac{16}{6}+12x$$

Since -\frac{105}{6} and \frac{16}{6} have the same denominator, add them by adding their numerators.

$$15x+\frac{-105+16}{6}+12x$$

Add -105 and 16 to get -89.

$$15x-\frac{89}{6}+12x$$

Combine 15x and 12x to get 27x.

$$27x-\frac{89}{6}$$