How would this equation be solved?

Question

Well, after looking through my Algebra I homework, I come to this problem:

A number plus five, divided by two, added to the quotient of that same number minus one, divided also by two, has a sum of that number minus one, divided by three.

Simply put, [(x+5)/2]+[(x-1)/2] equals [(x-1)/3].

These are all fractions, and when I solved it, I got a soultion of 3.5, which doesn't seem right. I multiplied the entire expression by the LCD, six, and divided the resulting binomials by the monomials in the denominator. It still doesn't seem right.

Did I make a mistake? How do I solve this?

Answer 1

(x + 5)/2 + (x - 1)/2 = (x - 1)/3

3(x + 5) + 3(x - 1) = 2(x - 1)

3x + 15 + 3x - 3 = 2x - 2

4x = - 14

x = - 3.5

I wonder if the equation accurately represents the word problem. I'm confused by the word "quotient" in the sentence??

Answer 2

There must have been some mistake somewhere with your calculations, you were right with your LCD. Let's try it:

this is (x+5)/2 + (x-1)/2 =(x-1)/3

then 6(x+5)/2 +6(x+1)/2 =6(x-1)/3

that is 3(x+5) + 3(x+1) = 2(x-1)

so 3x +15 +3x + 3 = 2x + 2

therefore 6x -2x = 2-18

=>4x = -16

=>4x/4 = -16/4

=> x = -4

Answer 3

X by 6 is correct, but the answer should be -3.5

LHS (-3.5 + 5)/2 + (-3.5-1)/2 = 1.5/2 - 4.5/2 = -3/2 = -1.5
RHS (-3.5 -1)/3 = -4.5/3 = -1.5