Solve 1/4-(x+1/2)-5/16

$$\frac { 1 } { 4 } - ( x + \frac { 1 } { 2 } ) - \frac { 5 } { 16 }$$

Evaluate

$$-x-\frac{9}{16}$$

Solution Steps

To find the opposite of x+\frac{1}{2}, find the opposite of each term.

$$\frac{1}{4}-x-\frac{1}{2}-\frac{5}{16}$$

Least common multiple of 4 and 2 is 4. Convert \frac{1}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{1}{4}-x-\frac{2}{4}-\frac{5}{16}$$

Since \frac{1}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-2}{4}-x-\frac{5}{16}$$

Subtract 2 from 1 to get -1.

$$-\frac{1}{4}-x-\frac{5}{16}$$

Least common multiple of 4 and 16 is 16. Convert -\frac{1}{4} and \frac{5}{16} to fractions with denominator 16.

$$-\frac{4}{16}-x-\frac{5}{16}$$

Since -\frac{4}{16} and \frac{5}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-4-5}{16}-x$$

Subtract 5 from -4 to get -9.

$$-\frac{9}{16}-x$$

Expand

$$-x-\frac{9}{16}$$

Solution Steps

To find the opposite of x+\frac{1}{2}, find the opposite of each term.

$$\frac{1}{4}-x-\frac{1}{2}-\frac{5}{16}$$

Least common multiple of 4 and 2 is 4. Convert \frac{1}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{1}{4}-x-\frac{2}{4}-\frac{5}{16}$$

Since \frac{1}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-2}{4}-x-\frac{5}{16}$$

Subtract 2 from 1 to get -1.

$$-\frac{1}{4}-x-\frac{5}{16}$$

Least common multiple of 4 and 16 is 16. Convert -\frac{1}{4} and \frac{5}{16} to fractions with denominator 16.

$$-\frac{4}{16}-x-\frac{5}{16}$$

Since -\frac{4}{16} and \frac{5}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-4-5}{16}-x$$

Subtract 5 from -4 to get -9.

$$-\frac{9}{16}-x$$