Solve algebraically for x: (x + 2)/6 = 3/(x - 1)

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Given:-

(x + 2)/6 = 3/(x - 1)

or, (x+2)*(x-1) = 3*6

or, (x^2) + x - 2 = 18

or,  (x^2) + x - 20 = 0

or, (x^2) + 5x - 4x - 20 = 0

or, x(x+5) - 4(x+5) = 0

or, (x-4)*(x+5) = 0

or, x = 4 

or, x = -5

Approved by eNotes Editorial Team
An illustration of the letter 'A' in a speech bubbles

We have to solve (x + 2)/6 = 3/(x - 1) for x.

(x + 2)/6 = 3/(x - 1)

=> (x + 2)(x - 1) = 3*6

=> x^2 + 2x - x - 2 = 18

=> x^2 + x - 20 = 0

=> x^2 + 5x - 4x - 20 = 0

=> x(x + 5) - 4(x + 5) = 0

=> (x - 4)(x + 5) = 0

=> x = 4 and x = -5

The solution of the equation is x = 4 and x = -5

Approved by eNotes Editorial Team