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

Question 352194: Hello!
I have to solve for the inequality
I figured I would multiply 2x+3 to both sides, so I'll end up getting:

If I distribute the 2, then I would end up getting:

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)   (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
which will never be true. So that mneas there is no solution!
Answer by Fombitz(32388)   (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.

which holds when

.
.
.

Answer by ewatrrr(24785)   (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

RELATED QUESTIONS
Hello My name is Aj and this is my problem: I must "Solve for given variable" (I... (answered by jim_thompson5910,solver91311)
Multiply. (-4x)^2 (2x^3)^3 I'm getting confused with what looks to me to be extra... (answered by xUser)
Hello. Can you help me with this equation? 2x-3/(x+4)=x-3/x-4 I have tried to... (answered by Boreal)
How do I solve this equation, 4x - 7 = 2x - 7 I added 7 to both sides, so it looks... (answered by macston)
Solve each exponential equation for x. Round your answer to 3 decimal places. a) 9 ^... (answered by richard1234)
When it comes to solving Rational Functions, I get lost when I have a Sum and Product... (answered by rwm)
I keep getting stomped on how to solve equations like 3x^1/3 + 2x^2/3 = 5 i get it into... (answered by jsmallt9)
A triangular sail has an area of x^2 + 5x +6 square meters and a height of x + 3 meters.... (answered by Earlsdon)
Hi there, I am confronted with the following question: "Solve the inequality and... (answered by longjonsilver)