How do you solve 6-3(x+3)>10-2x63(x+3)>102x?

1 Answer
Nov 2, 2017

x<-13x<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<21<2. If we multiply both sides of this inequality by -11, 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<-21<2, which is clearly false! To preserve the truth of the inequality, we need to flip the sign when we flip the numbers; -1> -21>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 xx:

6-3(x+3)>10-2x63(x+3)>102x
6-3x-9>10-2x63x9>102x (distribute on the left side)
-3-3x>10-2x33x>102x (simplify)
-3>10+x3>10+x (add 3x3x to both sides)
-13>x13>x (subtract 10 from both sides)

x<-13x<13