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Question 129539: 3x-9< 2x-6
i have a whole paper..i need help with all of it... :[
Found 2 solutions by jim_thompson5910, ilana:
Answer by jim_thompson5910(35256)   (Show Source):
Answer by ilana(307) (Show Source):
You can put this solution on YOUR website! If you know how to solve equations for x, inequalities are almost the same. The only thing that changes is you have switch the sign if you multiply or divide by a negative number. If the sign really worries you, you can pretend it's an equation and then figure out the sign at the end. I will show you both ways.
3x-9<2x-6
Subtract 2x from both sides to get the x terms together.
x-9<-6
Add 9 to both sides to get the constant terms together. Remember, the sign stays the same for addition/subtraction. It only changes for multiplication/division.
x<3
THAT IS YOUR SOLUTION (I AM WRITING A LOT MORE SO I WANT YOU TO SEE THIS)
Check: Try a number less than 3 to make sure it works. See if x=0 makes the original inequality true.
3x-9<2x-6
3(0)-9<2(0)-6
0-9<0-6
-9<-6
This is true, so it works.
If you do not want to deal with the inequality sign, pretend it's an equation.
3x-9<2x-6
3x-9=2x-6
Solve: x-9=-6, x=3.
Now try numbers bigger than and less than 3 to decide which way the sign goes.
Try x=0 and x=5.
3(0)-9 < ? 2(0)-6
-9 < ? -6 This is true, so x must be less than 3, so x<3 is the solution.
Try x=5:
3(5)-9 < ? 2(5)-6
15-9 < ? 10-6
9 < ? 4
This is not true, so we can see x cannot be greater than 3. This just confirms what we already found out.
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