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

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

Evaluate

$$-\frac{11x}{2}-\frac{5}{12}$$

Solution Steps

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

$$\frac{9}{4}-8x-2\times \frac{4}{3}+\frac{5}{2}x$$

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

$$\frac{9}{4}-8x+\frac{-2\times 4}{3}+\frac{5}{2}x$$

Multiply -2 and 4 to get -8.

$$\frac{9}{4}-8x+\frac{-8}{3}+\frac{5}{2}x$$

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

$$\frac{9}{4}-8x-\frac{8}{3}+\frac{5}{2}x$$

Least common multiple of 4 and 3 is 12. Convert \frac{9}{4} and \frac{8}{3} to fractions with denominator 12.

$$\frac{27}{12}-8x-\frac{32}{12}+\frac{5}{2}x$$

Since \frac{27}{12} and \frac{32}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-32}{12}-8x+\frac{5}{2}x$$

Subtract 32 from 27 to get -5.

$$-\frac{5}{12}-8x+\frac{5}{2}x$$

Combine -8x and \frac{5}{2}x to get -\frac{11}{2}x.

$$-\frac{5}{12}-\frac{11}{2}x$$

Expand

$$-\frac{11x}{2}-\frac{5}{12}$$

Solution Steps

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

$$\frac{9}{4}-8x-2\times \frac{4}{3}+\frac{5}{2}x$$

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

$$\frac{9}{4}-8x+\frac{-2\times 4}{3}+\frac{5}{2}x$$

Multiply -2 and 4 to get -8.

$$\frac{9}{4}-8x+\frac{-8}{3}+\frac{5}{2}x$$

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

$$\frac{9}{4}-8x-\frac{8}{3}+\frac{5}{2}x$$

Least common multiple of 4 and 3 is 12. Convert \frac{9}{4} and \frac{8}{3} to fractions with denominator 12.

$$\frac{27}{12}-8x-\frac{32}{12}+\frac{5}{2}x$$

Since \frac{27}{12} and \frac{32}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-32}{12}-8x+\frac{5}{2}x$$

Subtract 32 from 27 to get -5.

$$-\frac{5}{12}-8x+\frac{5}{2}x$$

Combine -8x and \frac{5}{2}x to get -\frac{11}{2}x.

$$-\frac{5}{12}-\frac{11}{2}x$$