Solve and show work for each proportion.
2x-2/14 = 2x-4/6
x+2/6 = x-1/12
Get rid of the denominators. For example, in the second equation, multiply both sides by 12.
12x + 4 = 12x - 1
However, there is no solution, since the 12x's cancel each other out. The same is true of the first equation. Do you have typos?
To solve for x in each proportion, we need to cross-multiply and then solve for x.
1. 2x-2/14 = 2x-4/6:
Cross-multiplying, we get:
(2x - 2) * 6 = (2x - 4) * 14
Simplifying both sides of the equation, we have:
12x - 12 = 28x - 56
Moving the variable terms to one side and the constant terms to the other side:
12x - 28x = -56 + 12
-16x = -44
Dividing both sides of the equation by -16:
x = -44 / -16
Simplifying the fraction:
x = 11 / 4
Therefore, x = 2.75.
2. x+2/6 = x-1/12:
Cross-multiplying, we get:
(x + 2) * 12 = (x - 1) * 6
Simplifying both sides of the equation, we have:
12x + 24 = 6x - 6
Moving the variable terms to one side and the constant terms to the other side:
12x - 6x = -6 - 24
6x = -30
Dividing both sides of the equation by 6:
x = -30 / 6
Simplifying the fraction:
x = -5
Therefore, x = -5.
The solutions to the given proportions are x = 2.75 and x = -5, respectively.