Solve 7/w-3=-1/4w-12+2

$$\frac { 7 } { w - 3 } = - \frac { 1 } { 4 w - 12 } + 2$$

Solve for w

$$w = \frac{53}{8} = 6\frac{5}{8} = 6.625$$

Steps for Solving Linear Equation

Variable w cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 4\left(w-3\right), the least common multiple of w-3,4w-12.

$$4\times 7=-1+4\left(w-3\right)\times 2$$

Multiply 4 and 7 to get 28.

$$28=-1+4\left(w-3\right)\times 2$$

Multiply 4 and 2 to get 8.

$$28=-1+8\left(w-3\right)$$

Use the distributive property to multiply 8 by w-3.

$$28=-1+8w-24$$

Subtract 24 from -1 to get -25.

$$28=-25+8w$$

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

$$-25+8w=28$$

Add 25 to both sides.

$$8w=28+25$$

Add 28 and 25 to get 53.

$$8w=53$$

Divide both sides by 8.

$$w=\frac{53}{8}$$