Find equivalent expressions

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Updated April 24, 2017

By Pharaba Witt

Algebra strikes fear in the hearts of many both grown and still in school. Finding equivalent expressions is not as complicated or as daunting as you might think. It comes down to taking the distributive property and working with it to find another way to say the same thing, mathematically.

Using Distributive Property

Start with an algebraic expression. Using the example 2x(3y + 2) will make it easier to walk through the process.

Distribute the multiple 2x throughout the rest of the equation. This means multiplying 2x by 3y and by 2. Multiply 2x and 3y and you get 6xy. Multiply 2x by 2 and you get 4x.

Complete the equation by putting it back together. This means taking the two new numbers and keeping the function in the middle the same: 6xy + 4x. This is your equivalent expression. You can write the two expressions to show equality: 2x(3y + 2) = 6xy + 4x.

Using Factoring

Identify the common factors in the parts of the equation. Breaking down the equation might be necessary to find an equivalent expression. If you were given the expression 6xy + 4x, you would need to work it the other direction by taking out the common numbers. In this case both numbers are divisible by 2.

Take out the first common number: 2(3xy + 2x). Now you see there is still another common factor, x.

Take out additional common factors: 2x(3y + 2). This gives you the equivalent expression. Again you end with 6xy + 4x = 2x(3y + 2).

Step-by-step explanation:

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

ratio is 2 : 9

the answer is three

13.5 : 3