# 4-3x<=14 if i solve for x on the right side of the equation, I get -3.33<x; if i solve for it on the left side, i get x<-3.33.  they can't both be right!! help please!

tjbrewer | Certified Educator

It looks to me like you forgot to reverse the inequality when you divided by -3.

We start with your inequality `4-3x<=14` To solve for x on the left side of the inequality we subtract the 4 from both sides `4-4-3x<=14-4` this gives us `-3x<=10` Then we divide both sides by -3, because we are dividing by a negative we reverse the inequality, this gives us `x>=-3 1/3`

Then to solve on the right side of the inequality, we start again with `4-3x<=14` we then add 3x to each side, to get the x on the other side of the inequality `4-3x+3x<=14+3x` simplifies to `4<=14+3x` We then subtract 14 from each side to isolate the term x. `4-14<=14-14+3x` simplify to get `-10<=3x` We then divide each side by 3, and we don't reverse the inequalithy because we are dividing by a positive, `-3 1/3<=x`

steveschoen | Certified Educator

Hi, teebs,

Don't forget.  When you multiply or divide an inequality by a negative number, you switch the direction of the arrow.  One of the two ways you did it, you would have had to divide by -3.  So, that would switch the direction of the arrow.

Good luck, teebs.  I hope this helps.

Till Then,

Steve

teebs | Student

thank you very much.

ornate | Student

The correct answer is x > -3.33, or x > -10/3.

The reason you got two different answers is because when you solved for it on the left side, you didn't flip the less than sign to a greater than sign. You were supposed to flip it because you divided both sides by a negative.

I hope this helps! :)