Solve 1/4a+11/15=-1/10

$$\frac { 1 } { 4 } a + \frac { 11 } { 15 } = - \frac { 1 } { 10 }$$

Solve for a

$$a = -\frac{10}{3} = -3\frac{1}{3} \approx -3.333333333$$

Steps for Solving Linear Equation

Subtract \frac{11}{15} from both sides.

$$\frac{1}{4}a=-\frac{1}{10}-\frac{11}{15}$$

Least common multiple of 10 and 15 is 30. Convert -\frac{1}{10} and \frac{11}{15} to fractions with denominator 30.

$$\frac{1}{4}a=-\frac{3}{30}-\frac{22}{30}$$

Since -\frac{3}{30} and \frac{22}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}a=\frac{-3-22}{30}$$

Subtract 22 from -3 to get -25.

$$\frac{1}{4}a=\frac{-25}{30}$$

Reduce the fraction \frac{-25}{30} to lowest terms by extracting and canceling out 5.

$$\frac{1}{4}a=-\frac{5}{6}$$

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$a=-\frac{5}{6}\times 4$$

Express -\frac{5}{6}\times 4 as a single fraction.

$$a=\frac{-5\times 4}{6}$$

Multiply -5 and 4 to get -20.

$$a=\frac{-20}{6}$$

Reduce the fraction \frac{-20}{6} to lowest terms by extracting and canceling out 2.

$$a=-\frac{10}{3}$$