Question

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

Answer 1

`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`