Proportion

How to solve a proportion (colon form, fraction form): 2 examples and their solutions.

Example 1

Example

Solution

To solve a proportion in colon form,
set
the product of the outer numbers, (2x + 1)⋅2
and the product of the inner numbers, 3⋅x
are equal.
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.

Example 2

Example

Solution

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.