Question

Solve the equation. Check the solution. g+4/g-2 = g-5/g-8

A.) -22/3
B.) 22
C.) -22
D.) 14
Please and Thank you :)

Answer 1

(g + 4)/(g - 2) = (g - 5)/(g - 8)
cross multiply
(g + 4)(g - 8) = (g - 5)(g - 2)
expand
g^2 - 4g - 32 = g^2 - 7g + 10
- g^2
-4g - 32 = -7g + 10
+ 7g
3g - 32 = 10
+ 32
3g = 42
÷ 3
g = 14

I hope this helps!

Answer 2

Option (d) is correct.

g = 14

Explanation:

Given:
`(g+4)/(g-2) =(g-5)/(g-8)`

We have to solve for g.

Consider the given expression
`(g+4)/(g-2) =(g-5)/(g-8)`

Apply cross multiply rule,

`if\:}(a)/(b)=(c)/(d)\mathrm{\:then\:}a\cdot \:d=b\cdot \:c`

We have

`\left(g+4\right)\left(g-8\right)=\left(g-2\right)\left(g-5\right)`

Apply distributive rule,

`\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd`

`\left(g+4\right)\left(g-8\right)=gg+g\left(-8\right)+4g+4\left(-8\right)`

Simplify, we get,

`\left(g+4\right)\left(g-8\right)=g^2-4g-32`

Similarly,
`\left(g-2\right)\left(g-5\right)=g^2-7g+10`

Substitute back, we have,

`g^2-4g-32=g^2-7g+10`

Simplify, we have,

`g^2-4g=g^2-7g+42`

Further simplification give,
`3g=42`

Divide both side by 3,

We have g = 14

Thus, Option (d) is correct.