Solve 7/w=8/w-1/5

$$\frac { 7 } { w } = \frac { 8 } { w } - \frac { 1 } { 5 }$$

Solve for w

$$w=5$$

Steps for Solving Linear Equation

Variable w cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5w, the least common multiple of w,5.

$$5\times 7=5\times 8+5w\left(-\frac{1}{5}\right)$$

Multiply 5 and 7 to get 35.

$$35=5\times 8+5w\left(-\frac{1}{5}\right)$$

Multiply 5 and 8 to get 40.

$$35=40+5w\left(-\frac{1}{5}\right)$$

Cancel out 5 and 5.

$$35=40-w$$

Swap sides so that all variable terms are on the left hand side.

$$40-w=35$$

Subtract 40 from both sides.

$$-w=35-40$$

Subtract 40 from 35 to get -5.

$$-w=-5$$

Multiply both sides by -1.

$$w=5$$