Question 572140: 14/(x+4)=5-x
Answer by mathsmiles(68)   (Show Source):
You can put this solution on YOUR website! 14/(x+4)=5-x
The first thing I'd do is get rid of the (x+4) so we don't have a fraction anymore
Do that by multiplying both sides by (x+4) giving ...
14 = (5-x)(x+4) Now multiply out the parens using FOIL ...
14 = 5x + 20 - x^2 - 4x Rearranging the terms ...
14 = -x^2 + 5x - 4x + 20 Now combine the x terms ...
14 = -x^2 + x + 20 Now let's get all the factors on one side of the equation so we can solve. Subtract 14 from both sides ...
-x^2 + x + 6 = 0 I like to make the x^2 term positive, so let's multiply by (-1)
(-1)(-x^2 + x + 6) = 0
x^2 - x - 6 = 0
Now we need to factor into two multipliers:
(x _ _)(x _ _) = 0 where each _ represents something we need to figure out, both the operator and the term
Since the last term is negative, we know we need one of each + and - operators:
(x - _)(x + _) = 0
Now we need factors of 6 which are different by 1 to get the -x terms:
Factors of 6:
6 = 2 * 3 That'll do it!
Since we want the middle x term to be negative, let's place 3 in the negative paren giving:
(x - 3)(x + 2) = 0
Now we have two possibilities for x:
x-3 = 0 Adding 3 to each side:
x = 3
OR
x+2 = 0 Adding -2 to each side:
x = -2
Since your problem didn't specify positive or negative, either of these should work. Let's check:
14/(x+4)=5-x Substituting x=3
14/(3+4)= 5-3
14/7 = 5-3
2 = 2 Correct!
14/(x+4) = 5-x Substituting x=-2:
14/(-2+4) = 5-(-2) Converting the double negative on the right to positive:
14/(2)=5+2
14/2 = 7
7=7 Correct!
|
|
|
