# How do you solve 2z+5>=1475?

May 8, 2018

The answer is $z \ge 735$.

#### Explanation:

Begin by subtracting $5$ from both sides to get the $z$ term by itself. This gives you:

$2 z \ge 1470$

Then divide by $2$ on both sides to get $z$ by itself. This will give you:

$\textcolor{red}{z \ge 735}$

This can be checked by picking a value greater than $735$ and a value less than $735$ and testing them against the original inequality.

For example, let's try $600$ and $800$.

$600$ is less than $735$, so the inequality shouldn't work.
$2 z + 5 \ge 1475$
$2 \left(600\right) + 5 \ge 1475$
$1205 \ge 1475$ -- which is not true.

As for $800$, this should work because it is greater than $735$.
$2 z + 5 \ge 1475$
$2 \left(800\right) + 5 \ge 1475$
$1605 \ge 1475$ -- which is true.