a.	$\begin{align} 2x+8&=x+12\\[5pt] 2x-x&=12-8\\[5pt] &\underline{\underline{x=4 }}\\[5pt] \end{align}$	b.	$\begin{align}2(x-3)&=4\\[5pt] \frac{2(x-3)}{2}&=\frac{4}{2}\\[5pt] x-3&=2\\[5pt] x&=2+3\\[5pt] &\underline{\underline{x=5 }}\\[5pt] \end{align}$	c.	$\begin{align}5x-8&=2(3-x)\\[5pt] 5x-8&=6-2x\\[5pt] 5x+2x&=6+8\\[5pt] 7x&=14\\[5pt] x&=\frac{14}{2}\\[5pt] &\underline{\underline{x=2 }}\\[5pt] \end{align}$
d.	$\begin{align}2(y+3)&=3(y-1)\\[5pt] 2y+6&=3y-3\\[5pt] 3+6&=3y-2y\\[5pt] &\underline{\underline{y=9 }}\\[5pt] \end{align}$	e.	$\begin{align} 4-5(3-p)&=2(p-1)\\[5pt] 4-15+5p&=2p-2\\[5pt] -11+5p&=2p-2\\[5pt] 5p-2p&=-2+11\\[5pt] 3p&=9\\[5pt] &\underline{\underline{p=3 }}\\[5pt] \end{align}$	f.	$\begin{align} \frac{x}{2}+1&=3\\[5pt] \frac{x}{2}&=3-1\\[5pt] \frac{x}{2}&=2\\[5pt] x&=2\times2\\[5pt] &\underline{\underline{x=4 }}\\[5pt] \end{align}$
g.	$\begin{align} 5-\frac{x}{4}&=1\\[5pt] \frac{-x}{4}&=1-5\\[5pt] \frac{-x}{4}&=-4\\[5pt] x&=-4\times-4\\[5pt] &\underline{\underline{x=16 }}\\[5pt] \end{align}$	h.	$\begin{align} 3-\frac{2x}{5}&=1\\[5pt] \frac{-2x}{5}&=1-3\\[5pt] \frac{-2x}{5}&=-2\\[5pt] x&=\frac{5\times-2}{-2}\\[5pt] &\underline{\underline{x=5 }}\\[5pt] \end{align}$	i.	$\begin{align} \frac{x}{3}+\frac{x}{4}&=7\\[5pt] \frac{4x+3x}{12}&=7\\[5pt] \frac{7x}{12}&=7\\[5pt] x&=\frac{7\times 12}{7}\\[5pt] &\underline{\underline{x=12 }}\\[5pt] \end{align}$
j.	$\begin{align} \frac{5x-2}{4}&=2\\[5pt] 5x-2&=2\times 4\\[5pt] 5x-2&=8\\[5pt] 5x&=8+2\\[5pt] 5x&=10\\[5pt] x&=\frac{10}{5}\\[5pt] &\underline{\underline{x=2 }}\\[5pt] \end{align}$	k.	$\begin{align} \frac{(a-3)}{2}+1&=4\\[5pt] \frac{a-3}{2}&=4-1\\[5pt] \frac{a-3}{2}&=3\\[5pt] a-3&=3\times 2\\[5pt] a-3&=6\\[5pt] a&=6+3\\[5pt] &\underline{\underline{a=9 }}\\[5pt] \end{align}$	l.	$\begin{align} \frac{(x+1)}{2}+\frac{(x-3)}{4}&=\frac{1}{2}\\[5pt] 4\times \frac{(x+1)}{2}+4\times\frac{(x-3)}{4}&=4\times\frac{1}{2}\\[5pt] 2x+2+x-3&=2\\[5pt] 3x-1&=2\\[5pt] 3x&=2+1\\[5pt] 3x&=3\\[5pt] x&=\frac{3}{3}\\[5pt] &\underline{\underline{x=1 }}\\[5pt] \end{align}$

By studying this lesson you will be able to

Construct and solve simple equations with algebraic fractions.