What is the solution to the rational equation (x)/(2x-1) + 1/4 = 2/2x-1?

Question

anonymous · Answer

$$\frac{ x }{ 2x-1 } + \frac{ 1 }{ 4 } = \frac{ 2 }{ 2x-1 }$$

marihelenh · Answer

First, you need to get a common denominator.

anonymous · Answer

My options are here:

anonymous · Answer

ok so you'd multiply everything by 2x-1 right?

marihelenh · Answer

Yes, but also by 4, because that is a part of the denominator and it needs to equal the rest.

anonymous · Answer

ok so then what would that look like

tkhunny · Answer

FIRST, you write down $x \ne \dfrac{1}{2}$.

anonymous · Answer

like after you multiply everything by 2x-1, you multiply all that by 4?

marihelenh · Answer

$$(\frac{ x }{ 2x-1 })(\frac{ 4 }{ 4 })$$ $$(\frac{ 1 }{ 4 })(\frac{ 2x-1 }{ 2x-1 })$$ $$(\frac{ 2x }{ 2x-1 })(\frac{ 4 }{ 4 })$$

marihelenh · Answer

You need to solve these out, that way each has the same denominator.

anonymous · Answer

ohhh ok. so, i did mental math real quick and i thiiiink the answer is 9/2?

anonymous · Answer

or maybe 3/2. its kinda late so im tryna do this fast lol

anonymous · Answer

um is that correct? or should i try again

marihelenh · Answer

Just fill in your answers for x and check.

anonymous · Answer

kk ill finish in a sec

anonymous · Answer

ok im p sure it's 3/2

marihelenh · Answer

Yep! Great job!

anonymous · Answer

ok great thanks