# How do you solve the inequality -4z-7<9 ?

##### 2 Answers
Jul 21, 2018

$z > - 4$

#### Explanation:

$- 4 z - 7 < 9$

Add $\textcolor{b l u e}{4 z}$ to both sides:
$- 4 z - 7 \quad \textcolor{b l u e}{+ \quad 4 z} < 9 \quad \textcolor{b l u e}{+ \quad 4 z}$

$- 7 < 9 + 4 z$

Subtract $\textcolor{b l u e}{9}$ from both sides:
$- 7 \quad \textcolor{b l u e}{- \quad 9} < 9 + 4 z \quad \textcolor{b l u e}{- \quad 9}$

$- 16 < 4 z$

Divide both sides by $\textcolor{b l u e}{4}$:
$\frac{- 16}{\textcolor{b l u e}{4}} < \frac{4 z}{\textcolor{b l u e}{4}}$

$- 4 < z$

Therefore,
$z > - 4$

Hope this helps!

Jul 21, 2018

$z > - 4$

#### Explanation:

Our end goal is to isolate $z$, so let's start by adding $7$ to both sides. We're left with

$- 4 z < 16$

Next, to isolate $z$ further, let's divide both sides by $- 4$. Recall that when we apply a negative to an inequality, the sign flips.

We now have

$z > - 4$

Hope this helps!