# How do you solve -x/5+12<4 and graph on the number line?

Nov 15, 2016

$x > 40$

Notice that the 'blob' at the left hand side of the red line on the axis is $\textcolor{red}{\underline{\text{not filled in}}}$. This means that $x$ does not actually take on the value of 40.

#### Explanation:

Multiply both sides by (-1) to make the x term positive. Note that this act turns the inequality sign the other way round.

$- \frac{x}{5} + 12 < 4 \text{ "->" } + \frac{x}{5} - 12 > - 4$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Why does it turn the inequality round?}}$

Consider $a > 3$

In this instance $a$ is positive and greater than 3. So for example
$4 > 3$

What happens if we multiply by (-1) but not change the sign round? We get this: $- 4 > - 3$ Clearly this is wrong so we need to reverse the sign. Thus $\left(- 1\right) \left(a > 3\right) \text{ becomes } - a < - 3$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Continuing the answer}}$

Add 12 to both sides giving:

$\frac{x}{5} > 8$

Multiply each side by 5

$\text{ } \textcolor{g r e e n}{\underline{\overline{| \textcolor{w h i t e}{\frac{.}{.}} x > 40 \textcolor{w h i t e}{\frac{.}{.}} |}}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 