How do you solve the inequality #-2x + 3 >7#?

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Answer 1 · 2015-12-03T12:59:55

#x < -2#

To solve a linear inequality, you can mostly behave the same way as you do when solving linear equations, with two important equations:

each time you multiply both sides with a negative number or if you divide both sides by a negative number, you need to "turn" the greater/less sign, so, transform #<# into #># and vice versa
if you flip the sides of the equation, you also need to "turn" the greater/less sign.

With this knowledge, you can solve the inequality as follows:

#-2< + 3 > 7#

... add #-3# on both sides ...

#-2x > 4#

... divide by #-2# on both sides; don't forget to flip the inequality sign!

# x < -2#

So, the solution is #x < -2#.