solving 5/x + 2/x = 4 - 9/x; find 2 consec. even integers w/

[hockey97]

HI, I am studying for a test. Intermediate algebra. getting confused easily.

I have this equation, x + 9 = -4, which I know how to do:

x + 9 =  -4
   -9    -9
-----------
x     = -13

Now I have trouble with this:

1) 5/x + 2/x = 4 - 9/x

I know you have to multiply both sides but this is where I am stuck at. another problem I have is with worded problems.

2) Find 2 consecutive even integers such that seven times the first exceeds four times the second by 10.

the teacher told use the use x+2 , x+4 cause for even or odds they are every 2 numbers.

could you explain these problems?
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Edited by stapel -- Reason for edit: Correcting "formatting".

 

[Aladdin]

Re: studying for a test. Intermediate algebra.

HI, I am getting confused easily.

I have this equation which I know how to do: x+9= -4 now I have trouble with this: 5/x+2/x=4-9/x
-9 -9 I know you have to multiply both sides but this is where I am
x=-13 stuck at.


ok, 5/x+2/x+9/x=4 then

take (1/x)common factor > (1/x)(5+2+9)=4
: (1/x)=4/16
Reciprocal : x=16/4=4

 

[stapel]

I have trouble with this:

1) 5/x + 2/x = 4 - 9/x

As posted, the equation is as follows:

. . . . .\(\displaystyle \frac{5}{x}\, +\, \frac{2}{x}\, =\, 4\, -\, \frac{9}{x}\)

If this is what you meant, then a good first step in solving this rational equation would be to multiply through by the denominator "x":

. . . . .\(\displaystyle 5\, +\, 2\, =\, 4x\, -\, 9\)

Then solve the resulting linear equation.

2) Find 2 consecutive even integers such that seven times the first exceeds four times the second by 10.

the teacher told use the use x+2 , x+4 cause for even or odds they are every 2 numbers.

While evens are "two apart" (like 6 and 8, 14 and 16, etc), you don't have to start with the first number already being two more than some other number. Instead, the usual set-up is to use "x" (or "n" or whatever) for "the first" of the evens, and then "x + 2" for "the next" even.

could you explain these problems?

For a complete explanation, including worked examples, follow the link provided in the paragraph above. :wink: