$(x+2)/20=1/5$. What is $x$? $(x+2)/20=1/5$. I have been stuck on this problem and tried various solutions to no avail. Please help.
 A: $$
\frac{x+2}{20}=\frac{1}{5} \tag*{ – multiply both sides by $20$}
$$
$$
\frac{x+2}{1}=\frac{20}{5} \tag*{  – simplify}
$$
$$
x+2=4 \tag*{  – substract $2$ from both sides}
$$
$$
x=2 \tag*{  – the answer}
$$
A: Given the expression
$$(x+2)/20$$
Suppose that we knew the value of $x$, for example $x=38$. How would we evaluate the above expression? First we see some parentheses, so they need to be evaluated first. Next, the only operation left is a division, so we perform that next. The steps would be as follows
$$\begin{align}
(x+2)/20&=&(38+2)/20\\
&=&40/20\\
&=&2\\
\end{align}$$
Now suppose that instead of knowing the value of $x$ and not knowing the value of the result of the expression (i.e. the right-hand-side of the equations), that we knew the value of the result, with the value of $x$ being unknown. This time, we are not evaluating an expression; we are, in fact, unraveling the evaluation of an expression. This unraveling requires us to perform the operations in reverse order. Consider the equation
$$(x+2)/20 = 1/5$$
If we knew the value of $x$ we would add two and then divide by twenty to get $1/5$. To unravel this evaluation we would take the result, reverse the last step (i.e. reverse the division by 20 by multiplying by 20).
$$((x+2)/20)\cdot 20=(1/5)\cdot 20$$
which looks a bit confusing, so I'm going to replace the slashes with horizontal lines.
$$\frac{x+2}{20}\cdot 20=\frac{1}{5}\cdot 20$$
$$x+2=4$$
Next, we reverse the addition of 2 (by subtracting 2).
$$x+2-2=4-2$$
$$x=2$$
Just to recap, when evaluating an expression we follow the BEDMAS order of operations. When solving an equation (or unraveling an evaluation) we reverse the order and reverse the operations themselves (e.g. a division becomes a multiplecation; an addition becomes a subtraction, etc.).
A: In general, whenever dealing with a fraction equality such as$$\frac{a}{b} = \frac{c}{d},$$ remember the extremes rule: $$a \times d = b \times c.$$
Applied to your case, this gives $$5 \times (x+2) = 20\times 1$$ which we now expand to $$5x + 10 = 20$$ leading to $$5x = 10$$ and thus $$x=2.$$
