Solve -6w+3/2=-1/2w-6/5

$$- 6 w + \frac { 3 } { 2 } = - \frac { 1 } { 2 } w - \frac { 6 } { 5 }$$

Solve for w

$$w=\frac{27}{55}\approx 0.490909091$$

Steps for Solving Linear Equation

Add \frac{1}{2}w to both sides.

$$-6w+\frac{3}{2}+\frac{1}{2}w=-\frac{6}{5}$$

Combine -6w and \frac{1}{2}w to get -\frac{11}{2}w.

$$-\frac{11}{2}w+\frac{3}{2}=-\frac{6}{5}$$

Subtract \frac{3}{2} from both sides.

$$-\frac{11}{2}w=-\frac{6}{5}-\frac{3}{2}$$

Least common multiple of 5 and 2 is 10. Convert -\frac{6}{5} and \frac{3}{2} to fractions with denominator 10.

$$-\frac{11}{2}w=-\frac{12}{10}-\frac{15}{10}$$

Since -\frac{12}{10} and \frac{15}{10} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{11}{2}w=\frac{-12-15}{10}$$

Subtract 15 from -12 to get -27.

$$-\frac{11}{2}w=-\frac{27}{10}$$

Multiply both sides by -\frac{2}{11}, the reciprocal of -\frac{11}{2}.

$$w=-\frac{27}{10}\left(-\frac{2}{11}\right)$$

Multiply -\frac{27}{10} times -\frac{2}{11} by multiplying numerator times numerator and denominator times denominator.

$$w=\frac{-27\left(-2\right)}{10\times 11}$$

Do the multiplications in the fraction \frac{-27\left(-2\right)}{10\times 11}.

$$w=\frac{54}{110}$$

Reduce the fraction \frac{54}{110} to lowest terms by extracting and canceling out 2.

$$w=\frac{27}{55}$$