To solve the proportion, we will start by using the Cross Products Property. Remember that we will need to treat x-3 as a single quantity in the cross multiplication process.
Because both sides of the equation are the same, we know that our solution is correct!
Alternative Solution
When and When Not to Solve With Cross Multiplication
Another way to solve this type of equation — a proportion which contains algebraic expressions — is by using the Properties of Equality without starting with the Cross Products Property. Let's see how this would have worked with the given equation.
This process was much faster than our original solving method! So, when is it easier to use cross multiplication and when is it faster to solve without it? The general rule of thumb is to look at where the variable is located. If the variable is in the denominator, solving is quicker with cross multiplication. If the variable is in the numerator, solving is quicker without it.
Use Cross Multiplication? [0.8em]
c|c
2/x-3=7/4 & 8x+1/3=11/10 [0.8em]
Probably! & Maybe not?
