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

1 Answer
Dec 10, 2017

-4<=x<=-1

Explanation:

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

2-5x >= 7
2-5xcolor(red)(-2)>=7color(red)(-2)
-5x>=5
(-5x)/color(red)(-5)>=5/color(red)(-5) Note that here, since we divide by a negative we switch the sign around:
x<=-1

Now let's solve for the second one,

3-7x<=31
3-7xcolor(red)(-3)<=31color(red)(-3)
-7x<=28
(-7x)/color(red)(-7)<=28/color(red)(-7) Here again we must switch the sign around:
x>=-4

So now we have bounds for x to go from:

-4<=x<=-1

Hope this helps!