# How do you graph the inequality 6(y+1)< -x?

May 30, 2016

Supporting Brian's solution

Just another way of showing the inequality and a tip about method.

#### Explanation:

$\textcolor{b r o w n}{\text{You can manipulate an inequality the same way you do an equation.}}$ Just be mindful of this (by example and using numbers to make my point), suppose we had
$- 3 < 4$

If we multiply by $\left(- 1\right)$ but do not change the inequality we have

$+ 3 < - 4 \textcolor{red}{\text{ This is false!}}$

Be mindful of what the inequality is doing.

We should have had: $\left(- 1\right) \left(- 3 < 4\right) \to \textcolor{g r e e n}{3 > - 4}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Solving your question}}$

Given:

$6 y + 6 < - x$

Subtract 6 from both sides

$6 y < - x - 6$

Divide both sides by 6

$\frac{6}{6} y < - \frac{x}{6} - 1$

But $\frac{6}{6} = 1$

$y < - \frac{x}{6} - 1$