Solve -1/5-1/2w=1/3

$$- \frac { 1 } { 5 } - \frac { 1 } { 2 } w = \frac { 1 } { 3 }$$

Solve for w

$$w = -\frac{16}{15} = -1\frac{1}{15} \approx -1.066666667$$

Steps for Solving Linear Equation

Add \frac{1}{5} to both sides.

$$-\frac{1}{2}w=\frac{1}{3}+\frac{1}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{1}{5} to fractions with denominator 15.

$$-\frac{1}{2}w=\frac{5}{15}+\frac{3}{15}$$

Since \frac{5}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$-\frac{1}{2}w=\frac{5+3}{15}$$

Add 5 and 3 to get 8.

$$-\frac{1}{2}w=\frac{8}{15}$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}.

$$w=\frac{8}{15}\left(-2\right)$$

Express \frac{8}{15}\left(-2\right) as a single fraction.

$$w=\frac{8\left(-2\right)}{15}$$

Multiply 8 and -2 to get -16.

$$w=\frac{-16}{15}$$

Fraction \frac{-16}{15} can be rewritten as -\frac{16}{15} by extracting the negative sign.

$$w=-\frac{16}{15}$$