SOLUTION: Hello! I have to solve for the inequality {{{(4x)/(2x+3)>2}}} I figured I would multiply 2x+3 to both sides, so I'll end up getting: {{{4x>2(2x+3)}}} If I distribute the 2, the

Algebra ->  Inequalities -> SOLUTION: Hello! I have to solve for the inequality {{{(4x)/(2x+3)>2}}} I figured I would multiply 2x+3 to both sides, so I'll end up getting: {{{4x>2(2x+3)}}} If I distribute the 2, the      Log On


   



Question 352194: Hello!
I have to solve for the inequality %284x%29%2F%282x%2B3%29%3E2
I figured I would multiply 2x+3 to both sides, so I'll end up getting:
4x%3E2%282x%2B3%29
If I distribute the 2, then I would end up getting:
4x%3E4x%2B6
But here lies the problem. I can't get both x's on one side because they'd just cancel each other out. So then I'm left with 0>6 which is false. So I feel like I approached this incorrectly.
What am I doing wrong?

Found 3 solutions by sofiyac, Fombitz, ewatrrr:
Answer by sofiyac(983) About Me  (Show Source):
You can put this solution on YOUR website!
You are not doing anything wrong. In your case, the x's cancel out and you have
0%3E6 which will never be true. So that mneas there is no solution!

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
By multiplying the denominator, you lose the information contained within it.
Numbers are OK since you know the value, but variable expressions are unknown (could be positive, could be negative).
Go this way instead.
%284x%29%2F%282x%2B3%29%3E2
%284x%29%2F%282x%2B3%29-2%3E0
%284x%29%2F%282x%2B3%29-%28%282%282x%2B3%29%29%2F%282x%2B3%29%29%3E0
%284x%29%2F%282x%2B3%29-%28%284x%2B6%29%2F%282x%2B3%29%29%3E0
%284x-%284x%2B6%29%29%2F%282x%2B3%29%29%3E0
%284x-4x-6%29%2F%282x%2B3%29%29%3E0
%28-6%29%2F%282x%2B3%29%29%3E0
which holds when
2x%2B3%3C0
2x%3C-3
highlight%28x%3C-3%2F2%29
.
.
.




Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
*Note: In this case one cannot multiply the right hand side by (2x-3) because the value of x is unknown. Since x may be either positive or negative, you can't know whether to leave the inequality sign as <, or reverse it to >.
.
When Solving an inequality with a variable in the denominator:
.
First Step:
Find when the denominator would equal zero:
2x + 3 = 0
x = -3/2
.
Second step:
Examine the results of replacing > with an = sign. That results in a false statement 0 = 6 as you found. As there is no solution when that = sign is used:
.
x < -3/2 are the only numbers that work in this inequality