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

1 Answer
TwOfSpades
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!

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