Solve 2/3(1-W/2)/1-frac{W{3}}=10/13

$$\frac { \frac { 2 } { 3 } ( 1 - \frac { W } { 2 } ) } { 1 - \frac { W } { 3 } } = \frac { 10 } { 13 }$$

Solve for W

$$W = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by 1-\frac{W}{2}.

$$\frac{\frac{2}{3}+\frac{2}{3}\left(-\frac{W}{2}\right)}{1-\frac{W}{3}}=\frac{10}{13}$$

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

$$\frac{\frac{2}{3}+\frac{-2W}{3\times 2}}{1-\frac{W}{3}}=\frac{10}{13}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{2}{3}+\frac{-W}{3}}{1-\frac{W}{3}}=\frac{10}{13}$$

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

$$\frac{\frac{2-W}{3}}{1-\frac{W}{3}}=\frac{10}{13}$$

Express \frac{\frac{2-W}{3}}{1-\frac{W}{3}} as a single fraction.

$$\frac{2-W}{3\left(1-\frac{W}{3}\right)}=\frac{10}{13}$$

Use the distributive property to multiply 3 by 1-\frac{W}{3}.

$$\frac{2-W}{3-3\times \frac{W}{3}}=\frac{10}{13}$$

Express -3\times \frac{W}{3} as a single fraction.

$$\frac{2-W}{3+\frac{-3W}{3}}=\frac{10}{13}$$

Cancel out 3 and 3.

$$\frac{2-W}{3-W}=\frac{10}{13}$$

Variable W cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 13\left(W-3\right), the least common multiple of 3-W,13.

$$-13\left(2-W\right)=10\left(W-3\right)$$

Use the distributive property to multiply -13 by 2-W.

$$-26+13W=10\left(W-3\right)$$

Use the distributive property to multiply 10 by W-3.

$$-26+13W=10W-30$$

Subtract 10W from both sides.

$$-26+13W-10W=-30$$

Combine 13W and -10W to get 3W.

$$-26+3W=-30$$

Add 26 to both sides.

$$3W=-30+26$$

Add -30 and 26 to get -4.

$$3W=-4$$

Divide both sides by 3.

$$W=\frac{-4}{3}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$W=-\frac{4}{3}$$