The Secret to Solving Equations with Variables on Both Sides

Get the free Solving Equations with Variables on Both Sides worksheet and other resources for teaching & understanding Solving Equations with Variables on Both Sides

Here’s How to Solve Equations with Variables on Both Sides

When solving Equations with Variables on Both Sides, you must follow certain steps. The first thing you must do is get all the variables on one side of the equation. In order to do this, you must use the addition and subtraction property of equality to add or subtract the term with the variable so that they are on the same side. The next step when solving Equations with Variables on Both Sides, is to get the constants on the other side of the equal sign. You also add or subtract a constant so that your constant gets cancelled on the same side as the variable on the equal sign. The last step when solving Equations with Variables on Both Sides is to divide both sides of the equation by the coefficient of the variable so that it will cancel out

Common Core Standard: 8.EE.C.7

Basic Topics: Combining Like Terms, Distributive Property, Two Step Equations, One Step Inequalities, Two Step Inequalities, Multi Step Inequalities

Return To: Home, 8th Grade

Solving Equations with Variables on Both Sides Worksheet

Are you wondering what’s the quickest way to learn how to solve an equation with variables on both sides? Then check out the following steps. When finding How to Solve Equations with Variables on Both Sides, you should follow certain steps. The first thing you should do is get every one of the factors on one side of the equations. To do this, you should use the addition and subtraction property of equality to add or subtract the term with the variable so they are on a same side. The final step when finding how to solve Equations with Variables on Both Sides, is to get the constants on the opposite side of the equation sign. You should add or subtract a constant with the goal that your constant gets dropped on opposite side from the variable on the equal sign. The last step when solving Equations with Variables on Both Sides is to divide the two sides of the equation by the coefficient of the variable so it will cancel out.

Equations with Variables on Both Sides Practice: 3 Steps

Steps for Solving the Equations with Variables on Both Sides Example above:

Add fifty three to both sides of the equation so that you get all constants on one side together.
Subtract five x from both sides.
Divide both sides of the equations by negative two to get your solution of negative thirty three.

Equations with Variables on Each Side Practice Problems Quiz

Solving Equations with Variables on Both Sides Worksheet Video

Watch our free video on how to solve Equations with Variables on Both Sides. This video shows how to solve problems that are on our free Solving Equations with x on Both Sides worksheet that you can get by submitting your email above.

Watch the free Equations with Variables on Both Sides video on YouTube here: How to Solve Equations with Variables on Both Sides Video

Video Transcript:

In this video we’re gonna work on some solving equations with variables on both sides practice problems from our solving equations with variables on both sides worksheets. Let’s jump to number one. Our first problem on our how to solve equations with variables on both sides worksheet gives us 4x minus 19 equals x plus 11. The first step in solving this equation with variables on both sides is to get all the constants on one side together. What we need to do is we need to add 19 here to this side plus 19 that the constant on this side will go away and that we have the constants on the same side together or only on one side. After we add 19 here the 19’s cancel and we bring down the 4 x on this side and we bring down the X on this side and then we’re going to combine 11 plus 19 which is 30. Then the next step is we need to get the variable on the same side together. In order to do that we need to subtract the X here and the reason we’re subtracting X is because we have to get the variables on the opposite side of the constant. If we subtracted 4x and put the 4x over here that wouldn’t work because they would be on the same side of the equal sign and we don’t want to do that we want to get the X or we want to get the variables on the opposite side of the equal sign. After you subtract this X to get rid of this X here. This X goes away we have 4 X minus 1 X which is 3 X. On this side and then we have 30 on this side. This 3x is like saying 3 times X. In order to get rid of this coefficient you have to divide by 3 because the opposite of 3 times something is to divide that same number by 3. We will divide this by three the X the threes cancel and you’re left with just X on this side and then a 30 divided by 3 is 10. Our solution to our first equation with variables on both sides is x equals 10.

Alright moving on to our next problem, which is number two on our solving equations variables on both sides worksheet. We have 2x minus 3 equals 11x minus 21. In this case the first thing we need to do is we need to get the constants on the same side together. In order to do that I’m going to add 3 here so that the constant on this side of the equal sign will go away. We use positive 3 because this is minus 3 they will cancel and you’re left with 2x on this side and then you bring down your 11x here and then negative 21 plus 3 is negative 18. The next step is to get rid of this 11x so we have to subtract 11x here, and once again the reason we’re subtracting 11x is because we have to get the X’s or the variables on one side of the equals sign and the constants on the other side of the equals sign. We subtract 11x here when you subtract 11x these X’s cancel 2x minus 9x is, I’m sorry 2x minus 11x, is negative 9x equals and then you bring down your negative 18 on this side. The last step is to divide both sides by negative 9 because the coefficient is negative 9. We have to cancel that out so you divide this side by negative 9. The negative 9s cancel and you’re left with on this side negative 18 divided by negative 9 which is positive 2. This is the second example of how to do equations with variables on both sides.

The last problem we’re going to work on on our multi step equations with variables on both sides worksheet is number five. Number five gives us 3x minus 53 equals 5x plus 13. The first step in solving this problem is to get all the constants on the same side together. We’re going to go ahead and add 53 here so that these guys will cancel and you’ll be left with 3x on this side and then you bring your 5x straight down and then 13 plus 53 is 66. Our next step is to get the variables on the opposite side of the constants. We’re going to subtract 5x here the 5x is canceled and you have 3x minus 5x which is negative 2 x equals 66 on this side. Then your final step is to get rid of this negative 2. We have to divide this side by negative 2 whatever you do to one side you do to the other. We divide over here by negative 2 these guys cancel you’re left with just x equals 60 6 divided by negative 2 which is negative 33. That is our solution to our last problem in our equations with variable on both sides worksheet and download the solving equations with variables on both sides notes for more practice.