Solve 2/3(x-5)-1/4(x-2)-9/2

$$\frac { 2 } { 3 } ( x - 5 ) - \frac { 1 } { 4 } ( x - 2 ) - \frac { 9 } { 2 }$$

Evaluate

$$\frac{5x}{12}-\frac{22}{3}$$

Solution Steps

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

$$\frac{2}{3}x+\frac{2}{3}\left(-5\right)-\frac{1}{4}\left(x-2\right)-\frac{9}{2}$$

Express \frac{2}{3}\left(-5\right) as a single fraction.

$$\frac{2}{3}x+\frac{2\left(-5\right)}{3}-\frac{1}{4}\left(x-2\right)-\frac{9}{2}$$

Multiply 2 and -5 to get -10.

$$\frac{2}{3}x+\frac{-10}{3}-\frac{1}{4}\left(x-2\right)-\frac{9}{2}$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}\left(x-2\right)-\frac{9}{2}$$

Use the distributive property to multiply -\frac{1}{4} by x-2.

$$\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x-\frac{1}{4}\left(-2\right)-\frac{9}{2}$$

Express -\frac{1}{4}\left(-2\right) as a single fraction.

$$\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x+\frac{-\left(-2\right)}{4}-\frac{9}{2}$$

Multiply -1 and -2 to get 2.

$$\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x+\frac{2}{4}-\frac{9}{2}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x+\frac{1}{2}-\frac{9}{2}$$

Combine \frac{2}{3}x and -\frac{1}{4}x to get \frac{5}{12}x.

$$\frac{5}{12}x-\frac{10}{3}+\frac{1}{2}-\frac{9}{2}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{10}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{5}{12}x-\frac{20}{6}+\frac{3}{6}-\frac{9}{2}$$

Since -\frac{20}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{5}{12}x+\frac{-20+3}{6}-\frac{9}{2}$$

Add -20 and 3 to get -17.

$$\frac{5}{12}x-\frac{17}{6}-\frac{9}{2}$$

Least common multiple of 6 and 2 is 6. Convert -\frac{17}{6} and \frac{9}{2} to fractions with denominator 6.

$$\frac{5}{12}x-\frac{17}{6}-\frac{27}{6}$$

Since -\frac{17}{6} and \frac{27}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{12}x+\frac{-17-27}{6}$$

Subtract 27 from -17 to get -44.

$$\frac{5}{12}x+\frac{-44}{6}$$

Reduce the fraction \frac{-44}{6} to lowest terms by extracting and canceling out 2.

$$\frac{5}{12}x-\frac{22}{3}$$

Expand

$$\frac{5x}{12}-\frac{22}{3}$$

Solution Steps

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

$$\frac{2}{3}x+\frac{2}{3}\left(-5\right)-\frac{1}{4}\left(x-2\right)-\frac{9}{2}$$

Express \frac{2}{3}\left(-5\right) as a single fraction.

$$\frac{2}{3}x+\frac{2\left(-5\right)}{3}-\frac{1}{4}\left(x-2\right)-\frac{9}{2}$$

Multiply 2 and -5 to get -10.

$$\frac{2}{3}x+\frac{-10}{3}-\frac{1}{4}\left(x-2\right)-\frac{9}{2}$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}\left(x-2\right)-\frac{9}{2}$$

Use the distributive property to multiply -\frac{1}{4} by x-2.

$$\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x-\frac{1}{4}\left(-2\right)-\frac{9}{2}$$

Express -\frac{1}{4}\left(-2\right) as a single fraction.

$$\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x+\frac{-\left(-2\right)}{4}-\frac{9}{2}$$

Multiply -1 and -2 to get 2.

$$\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x+\frac{2}{4}-\frac{9}{2}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x+\frac{1}{2}-\frac{9}{2}$$

Combine \frac{2}{3}x and -\frac{1}{4}x to get \frac{5}{12}x.

$$\frac{5}{12}x-\frac{10}{3}+\frac{1}{2}-\frac{9}{2}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{10}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{5}{12}x-\frac{20}{6}+\frac{3}{6}-\frac{9}{2}$$

Since -\frac{20}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{5}{12}x+\frac{-20+3}{6}-\frac{9}{2}$$

Add -20 and 3 to get -17.

$$\frac{5}{12}x-\frac{17}{6}-\frac{9}{2}$$

Least common multiple of 6 and 2 is 6. Convert -\frac{17}{6} and \frac{9}{2} to fractions with denominator 6.

$$\frac{5}{12}x-\frac{17}{6}-\frac{27}{6}$$

Since -\frac{17}{6} and \frac{27}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{12}x+\frac{-17-27}{6}$$

Subtract 27 from -17 to get -44.

$$\frac{5}{12}x+\frac{-44}{6}$$

Reduce the fraction \frac{-44}{6} to lowest terms by extracting and canceling out 2.

$$\frac{5}{12}x-\frac{22}{3}$$