+0  
 
0
224
1
avatar

Given \(\frac{14x+22}{x+2}=-3x+1\), compute the sum of all the possible values of \(x\). Express your answer as a fraction.

Guest Jun 16, 2017
edited by Guest  Jun 16, 2017
 #1
avatar
0

Solve for x:
(14 x + 22)/(x + 2) = 1 - 3 x

Multiply both sides by x + 2:
14 x + 22 = (1 - 3 x) (x + 2)

Expand out terms of the right hand side:
14 x + 22 = -3 x^2 - 5 x + 2

Subtract -3 x^2 - 5 x + 2 from both sides:
3 x^2 + 19 x + 20 = 0

The left hand side factors into a product with two terms:
(x + 5) (3 x + 4) = 0

Split into two equations:
x + 5 = 0 or 3 x + 4 = 0

Subtract 5 from both sides:
x = -5 or 3 x + 4 = 0

Subtract 4 from both sides:
x = -5 or 3 x = -4

Divide both sides by 3:
Answer: | x = -5         or          x = -4/3     

Guest Jun 16, 2017

12 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.