Solving for X fraction equations:

[PLAYNOISE]

I have four questions in my homework that I am just not understanding, its a review from algebra 1 and i just dont know where to start or end...these are the problems

1.) (5X/4) + (1/2) = X - (1/2)

2.) [(5x-4)/(5X+4)] = (2/3)

3.) [(7)/(2x+1)] - [(8x)/(2x-1)] = -4

4.) (1/x) + [(2)/(X-5) = 0


If you could help me with these ive been trying to do them for the past hour about and im just like completely frozen mentally...thankyou so much
<3

 

[stapel]

1) Subtract 1x from both sides; subtract 1/2 from both sides. Multiply by 4 to get rid of the fraction on x. Simplify for the final answer.

2) Multiply both sides by 3(5x + 4). (I am assuming that, contrary to the usual practice, "x" and "X" are the same variable.) Subract 10x from both sides. Add 12 to both sides. Divide by 5. Simplify.

3) Multiply through by (2x + 1)(2x - 1). Add 16x² to both sides. Solve the remaining linear equation as in (1) and (2).

4) Multiply through by x(x - 5). (I am assuming that, contrary to the usual practice, "x" and "X" are the same variable.) Solve the resulting linear equation as in (1) and (2).

If you get stuck, please reply showing how far you have gotten in following these instructions. Thank you.

Eliz.

 

[PLAYNOISE]

Hi thankyou that got me started however on number 2 i got lost with the multiplying i just dont know how to make the numbers work when i multiply them by 3(5x+4)...and with the last two as well im getting lost with the multiplying in the beginning...once again i just dont know how to plug those numbers in..thanks <3

 

[Denis]

Hi thankyou that got me started however on number 2 i got lost with the multiplying i just dont know how to make the numbers work when i multiply them by 3(5x+4)...and with the last two as well im getting lost with the multiplying in the beginning...once again i just dont know how to plug those numbers in..thanks <3

If a/b = c/d, then ad = bc : known as crisscross multiplication

Try your #2 that way; you get:
3(5x - 4) = 2(5X + 4)
OK?

 

[tkhunny]

2.) [(5x-4)/(5X+4)] = (2/3)

It is good to know that 3*(5X+4) is the LCD. It is NOT necessary to know that. If you are having trouble with that, then do it in smaller pieces.

[(5x-4)/(5X+4)] = (2/3)

Multiply by 3

[(5x-4)/(5X+4)]*3 = (2/3)*3
[(5x-4)/(5X+4)]*3 = 2

Multiply by 5X+4

(5X+4)*[(5x-4)/(5X+4)]*3 = (5X+4)*2
(5X+4)*(5x-4)*3 = (5X+4)*2

One thing that may help is to remember WHY you are doing what you are doing. I didn;t pick 3 and 5X+4 just for fun. I picked them BECAUSE they would get rid of the denominators for me. Make sure they do that. You do NOT have to go through a lengthy manipuation to get them to do that.

When I did this step (below) of simplification, I didn't even consider multiplying (5X+4) by all the other stuff in the numerator. I knew it was supposed to eliminate the Denominator, so I just did that.

(5X+4)*[(5x-4)/(5X+4)]*3 = (5X+4)*2
(5X+4)*(5x-4)*3 = (5X+4)*2