Solving Equations With Variables On Both Sides Worksheet Pdf

Solving equations with variables on both sides can seem intimidating at first, but with practice, anyone can master this skill. A worksheet is a great way to practice this concept and get more comfortable with the process. In this article, we'll go over everything you need to know about solving equations with variables on both sides and provide you with a free PDF worksheet to practice on.

Understanding Equations With Variables On Both Sides

An equation with variables on both sides is an equation that has variables on both the left and right sides. For example:

3x + 7 = 2x + 12

In this equation, there are variables on both the left (3x) and right sides (2x). The goal is to isolate the variable (in this case, x) on one side of the equation.

Steps for Solving Equations With Variables on Both Sides

Here are the steps to follow when solving an equation with variables on both sides:

Combine like terms on each side of the equation.
Get rid of the smaller variable by subtracting or adding it from both sides of the equation.
Get rid of the larger variable by subtracting or adding it from both sides of the equation.
If necessary, divide or multiply both sides of the equation to isolate the variable.

Example Problem

Let's use the example equation from earlier:

3x + 7 = 2x + 12

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Using the steps above, we can solve for x:

Combine like terms on each side of the equation.

3x - 2x = x
7 - 12 = -5

So the equation becomes:

x - 5 = 0

Get rid of the smaller variable by subtracting or adding it from both sides of the equation.

x - 5 + 5 = 0 + 5

So the equation becomes:

x = 5

So the solution to the equation 3x + 7 = 2x + 12 is x = 5.

Free Solving Equations With Variables On Both Sides Worksheet PDF

To get more practice with solving equations with variables on both sides, download this free worksheet PDF:

https://www.mathworksheets4kids.com/equations/variables-two-side-easy1.pdf

Tips for Success

Here are some tips to keep in mind when solving equations with variables on both sides:

Combine like terms before getting rid of any variables.
Always perform the same operation to both sides of the equation.
Be careful when dividing or multiplying by negative numbers. Remember that this will change the direction of the inequality sign (if there is one).
Practice, practice, practice! The more you practice, the easier it will become.

Conclusion

Solving equations with variables on both sides can be a challenge, but with practice, anyone can master this skill. Using a worksheet is a great way to get more comfortable with the process and hone your skills. Remember to always combine like terms and perform the same operation to both sides of the equation. With these tips and some practice, you'll be a whiz at solving equations with variables on both sides in no time!