Solve the equation. Check the solution.

Question

g plus four over g minus two equals g minus five over g minus eight
(1 point)
Responses

negative twenty-two over three
Image with alt text: negative twenty-two over three

22
22

–22
–22

14

Answer 1

To solve the equation, we first find a common denominator for both sides. The common denominator is (g-2)(g-8).

(g + 4)/(g - 2) = (g - 5)/(g - 8)
(g + 4)(g - 8) = (g - 5)(g - 2)
g^2 - 8g + 4g - 32 = g^2 - 2g - 5g + 10
Simplify the equation
g^2 - 4g - 32 = g^2 - 7g + 10
Rearrange the equation
3g = 42
g = 14

Therefore, the solution to the equation is g = 14. Now we substitute g = 14 in the original equation to check the solution:

(14 + 4)/(14 - 2) = (14 - 5)/(14 - 8)
18/12 = 9/6
3/2 = 3/2

The solution checks out, so g = 14 is correct.