I don't know where to begin on these problems...
2/3 (x+5) = 1/4 (x+2)
32(1/16x - 1/32)
$\displaystyle 2/3 (x+5) = 1/4 (x+2)$
Distribute the fraction
$\displaystyle \frac{2}{3}x+\frac{10}{3}=\frac{1}{4}x+\frac{2}{4}$
Combine the x's on one side and non-x's or numbers on the other side
$\displaystyle \left(\frac{2}{3}-\frac{1}{4}\right)x=\frac{2}{4}-\frac{10}{3}$
Find the lowest common denominators
$\displaystyle \left(\frac{8}{12}-\frac{3}{12}\right)x=\frac{6}{12}-\frac{40}{12}$
$\displaystyle \frac{5}{12}x=\frac{-34}{12}$
Multiply by 12
$\displaystyle 5x=-34$
Divide by 5
$\displaystyle x = \frac{-34}{5}$
Did that help?
Hi, endlesst0m! Distribution of multiplication over addition works the same way with fractions as it does with whole numbers. For example:
If you had $\displaystyle 5(x^2-3)$, you would distribute the 5 to get $\displaystyle 5\cdot x^2 - 5\cdot3=5x^2 - 15$.
The process is the same with fractions:
$\displaystyle \frac23(x+5)=\frac14(x+2)$
$\displaystyle \Rightarrow\frac23\cdot x+\frac23\cdot5=\frac14\cdot x+\frac14\cdot2$
$\displaystyle \Rightarrow\frac{2x}3+\frac{2\cdot5}3=\frac x4 +\frac{1\cdot2}4$
$\displaystyle \Rightarrow\frac{2x}3+\frac{10}3=\frac x4+\frac12$
Do you see it now?