Solve -1/2w-7/3=-7/5

$$- \frac { 1 } { 2 } w - \frac { 7 } { 3 } = - \frac { 7 } { 5 }$$

Solve for w

$$w = -\frac{28}{15} = -1\frac{13}{15} \approx -1.866666667$$

Steps for Solving Linear Equation

Add \frac{7}{3} to both sides.

$$-\frac{1}{2}w=-\frac{7}{5}+\frac{7}{3}$$

Least common multiple of 5 and 3 is 15. Convert -\frac{7}{5} and \frac{7}{3} to fractions with denominator 15.

$$-\frac{1}{2}w=-\frac{21}{15}+\frac{35}{15}$$

Since -\frac{21}{15} and \frac{35}{15} have the same denominator, add them by adding their numerators.

$$-\frac{1}{2}w=\frac{-21+35}{15}$$

Add -21 and 35 to get 14.

$$-\frac{1}{2}w=\frac{14}{15}$$

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

$$w=\frac{14}{15}\left(-2\right)$$

Express \frac{14}{15}\left(-2\right) as a single fraction.

$$w=\frac{14\left(-2\right)}{15}$$

Multiply 14 and -2 to get -28.

$$w=\frac{-28}{15}$$

Fraction \frac{-28}{15} can be rewritten as -\frac{28}{15} by extracting the negative sign.

$$w=-\frac{28}{15}$$