SOLUTION: I’m supposed to solve the below expression for X, but I can’t figure out what I’m doing wrong. I believe your supposed to multiply by the LCD to remove the fraction term. Then wh

Algebra ->  Algebra  -> Expressions -> SOLUTION: I’m supposed to solve the below expression for X, but I can’t figure out what I’m doing wrong. I believe your supposed to multiply by the LCD to remove the fraction term. Then wh      Log On

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Question 150558: I’m supposed to solve the below expression for X, but I can’t figure out what I’m doing wrong. I believe your supposed to multiply by the LCD to remove the fraction term. Then when I calculate, I’m completely lost. Maybe I’m using the wrong LCD.

Problem is x+3/6 - x/5 = 9x-5/30
LCD is 30, so I multiplied each term by 30
5(x+3) – 6x = 9x – 5
5x + 15 – 6x = 9x – 5
-x + 15 = 9x – 5
15 = 10x – 5
20 = 10x
x=10
*Answer in my book is x=2

Problem is: 4/x + 2/x+1 = 5
LCD is x(x+1), so I multiplied each term by x(x+1)
4(x+1) + 2x = 5x(x+1)
4x + 4 + 2x = 5x^2 + 5x
6x + 4 = 5x^2 + 5x
4 = 5x^2 + 5x – 6x
4 = 5x^2 – x
*Answer in my book is x=1

Problem is 24/8x - x/3 = 3-x/6
LCD is 24x, so I multiplied each term by 24x
72 – 8 = 4x(3-x)
72 – 8 = 12x – 4x^2
64 = 12x – 4x^2
*Answer in my book is x=3 or x=6

Problem is 6/4(x-2) + 1/4 = 4/x
LCD is 4(x-2), so I multiplied each term by 4(x-2)
6 + x – 2 = x(x-2)
4 + x = x^2 – 2x
4 + x = 0
x = -4
*Answer in my book is x=3 or x=6

Answer by jim_thompson5910(28550) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you going in the right direction.

# 1

Good so far until you reach the second to last step

20+=+10x


20%2F10+=+cross%2810%2F10%29x Divide both sides by 10.


2+=x Divide 10 into 20 to get 2

So the answer is x=2





# 2

You're off to a good start, I'll start where you left off.

4+=+5x%5E2+%96+x+ Start with the given equation.


0+=+5x%5E2+%96+x+-4 Subtract 4 from both sides.


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%285%29%28-4%29+%29%29%2F%282%285%29%29 Plug in a=5, b=-1, and c=-4


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%285%29%28-4%29+%29%29%2F%282%285%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%285%29%28-4%29+%29%29%2F%282%285%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--80+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-4%29 to get -80


x+=+%281+%2B-+sqrt%28+1%2B80+%29%29%2F%282%285%29%29 Rewrite sqrt%281--80%29 as sqrt%281%2B80%29


x+=+%281+%2B-+sqrt%28+81+%29%29%2F%282%285%29%29 Add 1 to 80 to get 81


x+=+%281+%2B-+sqrt%28+81+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%281+%2B-+9%29%2F%2810%29 Take the square root of 81 to get 9.


x+=+%281+%2B+9%29%2F%2810%29 or x+=+%281+-+9%29%2F%2810%29 Break up the expression.


x+=+%2810%29%2F%2810%29 or x+=++%28-8%29%2F%2810%29 Combine like terms.


x+=+1 or x+=+-4%2F5 Simplify.


So the solutions are x+=+1 or x+=+-4%2F5