SOLUTION: -(x-3)+2(x-1)<3(x+4)

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Question 9490: -(x-3)+2(x-1)<3(x+4)

Found 2 solutions by prince_abubu, rapaljer:
Answer by prince_abubu(198) About Me  (Show Source):
You can put this solution on YOUR website!
-%28x-3%29%2B2%28x-1%29+%3C+3%28x%2B4%29 <----- Start here

+-x+%2B+3+%2B+2x+-+2+%3C+3x+%2B+12+ <----- distribute to get rid of parentheses

+-x+%2B+1+%3C+3x+%2B+12+ <----- combine like terms on the left side

+1+%3C+4x+%2B+12+ <----- add x to both sides

+-11+%3C+4x+ <----- subtract 12 from both sides

+-11%2F4+%3C+x+ <----- divide both sides by 4.

+x+%3E+-11%2F4+ <---- We just rewrote it so that the variable ends up on the left side. Notice that we flipped the inequality. You only do this if you want to switch the sides of an inequality. This way, your "pac-man" has its mouth open on the same quantity regardless of positioning.

Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
I think prince abubu has a boo-boo! Recheck that solution for a careless error!

-(x-3)+2(x-1)<3(x+4)
-x + 3 + 2x - 2 < 3x + 12
x + 1 < 3x + 12

Personally, when solving inequalities, I prefer to keep the variables on the left side, and take numbers to the right side. When students DON'T do this, they tend to make more errors than the way I suggested!

So, let's subtract 3x from each side to get the variables on the left side:
x - 3x + 1 < 3x - 3x + 12
-2x + 1 < 12

Subtract 1 from each side:
-2x + 1 - 1 < 12 - 1
-2x < 11

Divide both sides by -2. This is a critical step, since you must CHANGE the direction of the inequality, because you divided (or multiplied) both sides by a NEGATIVE number!!
+%28-2x%29%2F-2+%3C+11%2F-2+
x%3E+-11%2F2

R^2 at SCC