# How do you solve this system of equations: 2- 5x \geq 7 and 3- 7x \leq 31?

Dec 10, 2017

$- 4 \le x \le - 1$

#### Explanation:

We want to get both equations equal to x, so let's start with the first one:

$2 - 5 x \ge 7$
$2 - 5 x \textcolor{red}{- 2} \ge 7 \textcolor{red}{- 2}$
$- 5 x \ge 5$
$\frac{- 5 x}{\textcolor{red}{- 5}} \ge \frac{5}{\textcolor{red}{- 5}}$ Note that here, since we divide by a negative we switch the sign around:
$x \le - 1$

Now let's solve for the second one,

$3 - 7 x \le 31$
$3 - 7 x \textcolor{red}{- 3} \le 31 \textcolor{red}{- 3}$
$- 7 x \le 28$
$\frac{- 7 x}{\textcolor{red}{- 7}} \le \frac{28}{\textcolor{red}{- 7}}$ Here again we must switch the sign around:
$x \ge - 4$

So now we have bounds for $x$ to go from:

$- 4 \le x \le - 1$

Hope this helps!