Solve -1/4w-1/3=3w-1/2

$$- \frac { 1 } { 4 } w - \frac { 1 } { 3 } = 3 w - \frac { 1 } { 2 }$$

Solve for w

$$w=\frac{2}{39}\approx 0.051282051$$

Steps for Solving Linear Equation

Subtract 3w from both sides.

$$-\frac{1}{4}w-\frac{1}{3}-3w=-\frac{1}{2}$$

Combine -\frac{1}{4}w and -3w to get -\frac{13}{4}w.

$$-\frac{13}{4}w-\frac{1}{3}=-\frac{1}{2}$$

Add \frac{1}{3} to both sides.

$$-\frac{13}{4}w=-\frac{1}{2}+\frac{1}{3}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$-\frac{13}{4}w=-\frac{3}{6}+\frac{2}{6}$$

Since -\frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$-\frac{13}{4}w=\frac{-3+2}{6}$$

Add -3 and 2 to get -1.

$$-\frac{13}{4}w=-\frac{1}{6}$$

Multiply both sides by -\frac{4}{13}, the reciprocal of -\frac{13}{4}.

$$w=-\frac{1}{6}\left(-\frac{4}{13}\right)$$

Multiply -\frac{1}{6} times -\frac{4}{13} by multiplying numerator times numerator and denominator times denominator.

$$w=\frac{-\left(-4\right)}{6\times 13}$$

Do the multiplications in the fraction \frac{-\left(-4\right)}{6\times 13}.

$$w=\frac{4}{78}$$

Reduce the fraction \frac{4}{78} to lowest terms by extracting and canceling out 2.

$$w=\frac{2}{39}$$