How do you solve \frac { w + 2} { 4} + \frac { 3w + 1} { 2} = - 3?

Jul 30, 2017

$w = - \frac{16}{7}$

Explanation:

Use inverse operations to isolate the variable $w$

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

$\iff$ ($\frac{3 w + 1}{2} = \frac{6 w + 2}{4}$ Gives us a common denominator)

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

$\iff$ Combining the fractions

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

$\iff$ Multiply both sides by $4$

$w + 2 + 6 w + 2 = - 12$

$\iff$ Combine like terms

$7 w + 4 = - 12$

$\iff$ Subtract $4$ from both sides

$7 w = - 16$

$\iff$ Divide both sides by $7$

$w = - \frac{16}{7}$