Question

PLease HELP!!!!!!!!!!!!!!!! THIS IS A SERIOUS ISSUE
1/8x+1/5x+1/8=31/40

Answer 1

\[\Large \frac{ 1 }{8x }+\frac{ 1 }{5x }+\frac{ 1 }{8 }=\frac{ 31}{40 }\]

Whenever you have an equation with fractions, start by multiplying both sides of the equation by the LCD of all the fractions. This will make all the fractions go away (kinda like magic! :) and you will be left with a much simpler equation.

So, what is the LCD of 8x, 5x, 8, and 40?

Answer 2

4

Answer 3

8x=4 5x=1 8=4 40=2

Answer 4

No. The LCD must be a multiple of ALL the denominators. It has to be an expression such that you can multiply EACH den'r by SOMETHING and produce the LCD.

NONE of these den'rs are multiples of 4.

Answer 5

then its 1

Answer 6

"8x=4 5x=1 8=4 40=2" ??? I'm not sure what you mean by this - none of these are true.

Answer 7

so theres no solution

Answer 8

No, it's never 1 (unless both den'rs are 1).

Answer 9

There is always an LCD. Slow down. Do you understand what LCD is? the lowest common multiple of all the den'rs

Answer 10

So you need something, such that:

LCD = ?(8x)
LCD = ?(5x)
LCD = ?(8)
LCD = ?(40)

So, at a minimum, it must have as FACTORS:
8x, 5x, 8, and 40

Answer 11

But some of those HAVE common factors. So the LCD doesn't need to include those common factors twice, just once.

Answer 12

2x4=8 1x5=5x 2x4=8 9x5=40

Answer 13

So the LCD has to be a multiple of 8x, and also a multiple of 8.

Well, if it's a multiple of 8x, then it IS a multiple of 8 - because anything that is a multiple of 8x has a factor of 8.

So "multiple of 8x" covers "multiple of 8".

It also need to be a multiple of 5x, so it needs to have a factor of 5. Now, since it's a multiple of 8x, it already has a factor of x, so it doesn't need that, AGAIN. so we just need to include a factor of 5.

So far we have: 5(8x) = 40x and that IS a multiple of 8x and of 8, and of 5x.

All that's left is that it be a multiple of 40, but 40x IS a multiple of 40, so we are "covered" there.

So we have: LCD=5*8x=40x

Do you understand that so far?

Answer 14

yes

Answer 15

"2x4=8 1x5=5x 2x4=8 9x5=40"

OK, I think you are doing a factorization here? Yes, that's basically right - you can do the factorization of each den'r to see what all the "unique" factors are. You need to include, in the LCD, each factor, the MOST number of times that it appears in any den'r.

Just don't forget about the x.

Your factorizations should be:
8x=2*2*2*x
5x=5*x
8=2*2*2
40=2*2*2*5

Those are the prime factorizations. So the LCD must have:
3 factors of 2
1 factor of 5
1 factor of x

Which gives us, as I said above, 40x.

Answer 16

okay

Answer 17

OK, do you understand now how to find the LCD? Because this is an important, and basic, concept.

Answer 18

Once you have the lcd, the point is to multiply both sides of your equation by it:

\(\Large 40x \left(\dfrac{ 1 }{8x }+\dfrac{ 1 }{5x }+\dfrac{ 1 }{8 }\right)=\left(\dfrac{ 31}{40 }\right) 40x\)

Answer 19

Make sure you distribute on the left side, because that's where the "magic happens". The den'rs, on both sides, will cancel.

Answer 20

i cant get the answer