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

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

Evaluate

$$-3x-\frac{61}{6}$$

Solution Steps

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

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

Multiply \frac{4}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

Divide 4 by 2 to get 2.

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

Express \frac{4}{3}\left(-2\right) as a single fraction.

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

Multiply 4 and -2 to get -8.

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

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

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

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

$$2x-\frac{8}{3}-\frac{5}{2}\times 2x-\frac{5}{2}\times 3$$

Cancel out 2 and 2.

$$2x-\frac{8}{3}-5x-\frac{5}{2}\times 3$$

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

$$2x-\frac{8}{3}-5x+\frac{-5\times 3}{2}$$

Multiply -5 and 3 to get -15.

$$2x-\frac{8}{3}-5x+\frac{-15}{2}$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$2x-\frac{8}{3}-5x-\frac{15}{2}$$

Combine 2x and -5x to get -3x.

$$-3x-\frac{8}{3}-\frac{15}{2}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{8}{3} and \frac{15}{2} to fractions with denominator 6.

$$-3x-\frac{16}{6}-\frac{45}{6}$$

Since -\frac{16}{6} and \frac{45}{6} have the same denominator, subtract them by subtracting their numerators.

$$-3x+\frac{-16-45}{6}$$

Subtract 45 from -16 to get -61.

$$-3x-\frac{61}{6}$$

Expand

$$-3x-\frac{61}{6}$$

Solution Steps

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

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

Multiply \frac{4}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

Divide 4 by 2 to get 2.

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

Express \frac{4}{3}\left(-2\right) as a single fraction.

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

Multiply 4 and -2 to get -8.

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

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

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

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

$$2x-\frac{8}{3}-\frac{5}{2}\times 2x-\frac{5}{2}\times 3$$

Cancel out 2 and 2.

$$2x-\frac{8}{3}-5x-\frac{5}{2}\times 3$$

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

$$2x-\frac{8}{3}-5x+\frac{-5\times 3}{2}$$

Multiply -5 and 3 to get -15.

$$2x-\frac{8}{3}-5x+\frac{-15}{2}$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$2x-\frac{8}{3}-5x-\frac{15}{2}$$

Combine 2x and -5x to get -3x.

$$-3x-\frac{8}{3}-\frac{15}{2}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{8}{3} and \frac{15}{2} to fractions with denominator 6.

$$-3x-\frac{16}{6}-\frac{45}{6}$$

Since -\frac{16}{6} and \frac{45}{6} have the same denominator, subtract them by subtracting their numerators.

$$-3x+\frac{-16-45}{6}$$

Subtract 45 from -16 to get -61.

$$-3x-\frac{61}{6}$$