Solve 7/4w-1/2=-6w-1/3

$$\frac { 7 } { 4 } w - \frac { 1 } { 2 } = - 6 w - \frac { 1 } { 3 }$$

Solve for w

$$w=\frac{2}{93}\approx 0.021505376$$

Steps for Solving Linear Equation

Add 6w to both sides.

$$\frac{7}{4}w-\frac{1}{2}+6w=-\frac{1}{3}$$

Combine \frac{7}{4}w and 6w to get \frac{31}{4}w.

$$\frac{31}{4}w-\frac{1}{2}=-\frac{1}{3}$$

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

$$\frac{31}{4}w=-\frac{1}{3}+\frac{1}{2}$$

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

$$\frac{31}{4}w=-\frac{2}{6}+\frac{3}{6}$$

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

$$\frac{31}{4}w=\frac{-2+3}{6}$$

Add -2 and 3 to get 1.

$$\frac{31}{4}w=\frac{1}{6}$$

Multiply both sides by \frac{4}{31}, the reciprocal of \frac{31}{4}.

$$w=\frac{1}{6}\times \frac{4}{31}$$

Multiply \frac{1}{6} times \frac{4}{31} by multiplying numerator times numerator and denominator times denominator.

$$w=\frac{1\times 4}{6\times 31}$$

Do the multiplications in the fraction \frac{1\times 4}{6\times 31}.

$$w=\frac{4}{186}$$

Reduce the fraction \frac{4}{186} to lowest terms by extracting and canceling out 2.

$$w=\frac{2}{93}$$