# Equations

 User:
Equations
Equations with fractions

Steps to solve an equation with fractions:

1. Rewrite without fractions by multiplying both sides by the least common denominator.
2. Combine like terms.
3. Collect variables on one side and constants on the other.
4. Divide by the coefficient of the variable.

$\frac{2}{3}x+10=\frac{1}{5}(x+36)\;\Rightarrow\;15\cdot\;(\frac{2}{3}x+10)=15\cdot(\frac{1}{5}(x+36))\;\Rightarrow$

$10x+150=3x+108\;\;\Rightarrow\;\;10x-3x=108-150\;\Rightarrow\;7x=-42\;\Rightarrow\;\;x=-6$

$\frac{x-1}{2}+\frac{x}{3}=2\;\Rightarrow\;\frac{6(x-1)}{2}+\frac{6x}{3}=6\cdot2\;\;\Rightarrow$

$\fs23(x-1)+2x=12\;\Rightarrow\;\;3x-3+2x=12\;\Rightarrow\;5x=15\;\Rightarrow\;\;x=3$

Solve for x:

 $\frac{-4(-8x+4)}{4}+\frac{4}{8}=\frac{-5(-4x-1)}{4}+\frac{10}{8}$ Solution: