How do you solve #6-3(x+3)>10-2x#?

1 Answer
Nov 2, 2017

#x<-13#

Explanation:

Solving inequalities is very similar to solving regular equations with unknowns - simply isolate your desired variable to solve it. There's one important consideration that inequalities demand, though: dividing or multiplying both sides of an inequality by a negative number "flips" the inequality sign.

For a quick example of why this makes sense, consider the inequality #1<2#. If we multiply both sides of this inequality by #-1#, we'd like for the inequality to remain true. If it doesn't, we're fundamentally changing our original statement. If we perform this operation without flipping the sign, though, we get #-1<-2#, which is clearly false! To preserve the truth of the inequality, we need to flip the sign when we flip the numbers; #-1> -2# works just fine.

While an important situation to consider, we can avoid it in this problem. Here, I'll walk through the steps taken to isolate #x#:

#6-3(x+3)>10-2x#
#6-3x-9>10-2x# (distribute on the left side)
#-3-3x>10-2x# (simplify)
#-3>10+x# (add #3x# to both sides)
#-13>x# (subtract 10 from both sides)

#x<-13#