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

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

Solve for w

$$w=-\frac{2}{45}\approx -0.044444444$$

Steps for Solving Linear Equation

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

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

Combine 7w and \frac{1}{2}w to get \frac{15}{2}w.

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

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

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

Since -\frac{2}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

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

Add -2 and 1 to get -1.

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

Multiply both sides by \frac{2}{15}, the reciprocal of \frac{15}{2}.

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

Multiply -\frac{1}{3} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$w=\frac{-2}{3\times 15}$$

Do the multiplications in the fraction \frac{-2}{3\times 15}.

$$w=\frac{-2}{45}$$

Fraction \frac{-2}{45} can be rewritten as -\frac{2}{45} by extracting the negative sign.

$$w=-\frac{2}{45}$$