How to solve a proportion (colon form, fraction form): 2 examples and their solutions.
ExampleColon Form. (2x + 1) : 3 = x : 2
To solve a proportion in colon form,
the product of the outer numbers, (2x + 1)⋅2
and the product of the inner numbers, 3⋅x
So (2x + 1)⋅2 = 3⋅x.
(2x + 1)⋅2 = 4x + 2
Multiply a Monomial and a Polynomial
3⋅x = 3x
Solve the equation 4x + 2 = 3x.
Then x = -2.
Linear Equation (One Variable)
So x = -2 is the answer.
ExampleFraction Form. x/2 = (4x - 1)/5
To solve a proportion in fraction form,
cross product the numbers:
x⋅5 = 2⋅(4x - 1).
x⋅5 = 5x
2⋅(4x - 1) = 8x - 2
Solve the equation 5x = 8x - 2.
Then x = 2/3.
So x = 2/3 is the answer.