﻿ Variables on Both Sides Worksheets
These worksheets will teach your students to solve variables on both sides of an equation.

These worksheets demonstrate the various skills needed to solve an equation when there are variables found on both sides of the equal sig. To solve this we will learn to use grouping or isolating the variables. We will start you off with working with two of the same variables in an equation. You will need to combine those values or like terms and then proceed from there. As we get more advanced, we will look at problems that involve two completely different variables and how to solve for each. Most of these problems follow the format of combine like terms and perform any needed operations. This will seem very difficult at first but will become a breeze in time.

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## Double Sides Lesson

Learn how to solve an equation that has a variable on each side of the equal sign. x + 33.24 = 9 - 2x. This lesson will walk through it. In these types of equation, both sides of the equation have a term with the variable. To isolate the variable, we need to get all the variable terms to one side and the constant terms to the other side. Next, we combine like terms and then isolate the variable by multiplying or dividing.

## Practice Worksheet

Follow the steps to write an equation from the statement given, then solve for x. Example: When a number is multiplied by 2 and 1 is subtracted from the result, the result is the same as the result of that number multiplied by 9 and subtracted from 120.

## Both Sides of the Equation Worksheet

Solve for each equation. Check by substituting your solution to the equation. This is an example of the types of problems that you will find here: x + 9 = 2x + 4

## Homework Worksheet

For each of the 10 problems write an equation and solve. These problems will give you a written math statement that will need to be converted to an equation and then you can complete them.

## Variable Doubles Worksheet

You will be given 10 problems like this: -15 + 12x = 5x + 7 - 3x. You can solve them any number of ways.

## Warm Up

For each, write an equation and solve. You will have math statements that you will need to convert to equations that have variables on both sides of the equal sign. Example: When you multiply a number by 12 and add 18 the result is the same as the product of the number and 3.

## How to Solve Equations with Variables on Both Sides?

Until now we have worried about solving equations that contain one unknown variable. We will now look at what to do if you have two variables in a problem and are working to find the value of the variables. In this series of problems we are working with a single variable that is found on either side of an equation. The first step is to get all the non-variable values of the equation to one side of the equation. Then you can place the variables together on the other side. Once you combine the variables, it gets pretty easy to solve. Students will work on solving for variables on each side of an algebraic equation using grouping, isolating, and balancing. The worksheets also provide several methods to check the answers. You can always just plug the value you found into the equation itself. If the equation turns out to be true, you are right. If the equation is false, time to go back to the drawing board.<br>

Have you ever seen letters in your math problems? In algebra, we often encounter variables in our mathematical equations. As we go higher in grade level, more variables start appearing, sometimes on both sides of the equal sign.

How do you solve equations with variables on both sides? Is there a trick to it? What should you know when solving these questions? We will answer all these questions for you.

What are Variables?

You might have encountered a few letters in your math equation. Those letters are called variables. Variables are letters that represent a specific unknown value. Your goal is to find the unknown value of the variable that proves the equation.

For example, in the question 3x = 15, x is the variable. There are 26 letters in the English alphabet. So, there can also be 26 kinds of variables that you may see in a math equation.

What are Equations?

An equation is a statement between two expressions showing that the two expressions are equal. The expressions can consist of variables and numbers.

In simple terms, an equation is any statement with an equal sign and two expressions on both sides of the equal sign.

An algebraic equation is considered solved when you have isolated and found a value for the variable. This value should verify the equation. To solve such an equation, you must follow a simple rule: whatever you do on one side of the equation, you must also do it on the other.

Another thing to remember when solving such a question is the PEMDAS rule. The PEMDAS rule shows the order of operations. The equation must be operated in a sequence of parenthesis, exponents, multiplication or division, then the addition or subtraction.

The BODMAS rule is also important in this case. It states the order as Brackets Open, Division, Multiplication, Addition, then Subtraction.

Steps to Follow

Step 1: The first thing you need to do is identify the variable. The variable you identify is the variable you need to find a value to.

Step 2: Then, remove the variable from one side. You can do that by either adding, subtracting, multiplying or dividing the value to both sides of the equation.

Step 3: Remove the consonants from one side of the equation, following the same method. Tip: cancel out the consonant on the same side as your variable. You need to isolate your variable to one side.

Step 4: if there is a coefficient with the vowel, remove that.

Step 5: Confirm your answer. You can confirm your solution by putting the value of the variable you got into the original equation. If both sides are equal, your value is correct.

Example: Solve 10a - 12 = 7a + 15

We identify our variable as a and need to remove the variable for one side

To do that, we subtract both sides with 7a

10a - 12 – 7a = 7a + 15 – 7a
3a - 12 = 15

Now, we remove the consonant from the left side by adding both sides with 12

3a - 12 + 12 = 15 + 12
3a = 27

Now, we remove the coefficient by dividing both sides with 3

3a/3 = 27/3
a = 9

to confirm our answer, we add the value of a we got to the original equation.

10a – 12 = 7a + 15
10(9) – 12 = 7(9) + 15
90 -12 = 63 + 15
78 = 78

Hence, confirmed.

Conclusion

If you know the trick, solving equations with variables on both sides is easy. But the most important thing to do is to practice. Once you’ve practiced enough, you will never forget how to solve them.