Praxis Core Prep: How to Solve for x and Other Variables

By Carla Kirkland, Chan Cleveland

You will need to be able to solve for x (or any variable) on the Praxis Core exam. Solving equations is an enormous part of algebra. Understanding how to do it puts you in an excellent position for conquering Praxis Core algebra completely.

To solve an equation, you need to get the variable by itself on one side of the equal sign (=). If you are solving for x, the goal is to work with the equation until you have x = something, like x = 4 or x = –12.

Notice that in both cases, x is by itself on one side of the equal sign and a value is on the other side. Once you reach that point correctly, you have solved the equation. The point of solving an equation is to determine what the variable equals.

To get a variable by itself on one side of the equal sign, you need to perform whatever operations are necessary. Then, if necessary, combine like terms so the variable is in only one term in the equation.

The next step is to undo everything that is being done to the variable by doing the opposite. Addition and subtraction are opposite operations, and multiplication and division are opposite operations. You can use opposite operations to undo each other.

Because the two sides of an equation are equal, anything done to one side of the equation must be done to the other side so the two sides will remain equal.

If you have a set of weights with 50 pounds on one side and 50 pounds on the other side and you want to add a certain amount of weight to one side, you must add the same amount of weight to the other side to keep the weights of the two sides equal.

The values on either side of an equation work the same way. If you add 10 to one side of an equation but not the other, the two sides will no longer be equal. An equation is wrong if its sides aren’t equal.

Here’s how you get a variable by itself to determine its value (also known as solving for x):

  1. Isolate the variable.

    Get all the x’s on one side of the equal sign and the numbers without variables on the other side.

  2. Combine like terms.

    Add or subtract all the x’s on one side; add or subtract whatever is on the other side of the equal sign.

  3. Divide both sides of the equation by whatever number (coefficient) is in front of the x (or other variable).

You can see how these steps work by solving for y in this equation: 3y – 12 = y + 6.

  1. Isolate the variable.

    Move the y to the left side of the equation by subtracting y from both sides. Move the 12 to the right side by adding it to both sides of the equation. This gives you 3yy = 6 + 12.

  2. Combine like terms.

    Do the operations to get 2y = 18.

  3. Divide both sides of the equation by whatever number (coefficient) is in front of the x.

    When you divide 18 by 2, you get 9. Therefore, y = 9. Problem solved!