How to Solve Math Problems With a Variable

One of the most important math concepts that middle school students will need to master is learning how to solve an equation that has a variable in it. A variable is a letter, usually the letter x or n, that represents an unknown number in an equation. The goal of solving the equation is to figure out what number the variable should be. While all of these equations are different, you will follow the same basic steps to solve them.

Difficulty: Moderately Easy

Instructions

Things You'll Need:

• Paper
• Pencil

How to Solve Math Problems With a Variable

1. Copy the equation exactly as it appears in the book onto your paper. For this example, use 3x + 5 = 39 + 2.

2. Simplify anything that can be simplified. In this equation, 39 + 2 should be added together. This gives you 3x + 5 = 41.

3. Identify the terms. Terms are the letter and number combinations that are separated by addition, subtraction or equal signs. In this example, the terms are 3x, 5 and 41.

4. Isolate the term that contains the variable. To eliminate the 5, you have to do the opposite operation than the one that is being done in the equation. In 3x + 5 = 41, the 5 is being added, so you need to subtract it (3x +5 - 5 = 41).

5. Subtract 5 from the other side of the equal sign in order to keep the equation balanced (3x + 5 - 5 = 41 - 5). This yields 3x + 0 = 36, or simply 3x = 36.

6. Isolate the variable itself. The 3 is being multiplied with x, so to eliminate the 3 you must divide that side of the equation by 3. This must also be repeated on the opposite side of the equal sign (3x/3 = 36/3).

7. Solve the equation. By dividing the 3 by 3, you get 1. Multiplying 1 by x yields x. Dividing 36 by 3 gives you 12. The answer to the equation is x = 12.

8. Check the equation by putting the 12 in for the variable (3 *12 + 5 = 41). If you have solved the equation correctly, the equation will be balanced. Since 3 * 12 + 5 does, in fact, equal 41, you are done.

Tips & Warnings

• Sometimes the answer will be a fraction. This is fine, provided you have solved the equation correctly.
• Always eliminate the terms that are being added or subtracted first, before dealing with any terms that are being divided or multiplied.
• Never do an action to one side of the equation without doing it to the other side of the equation.
• Always check your answer, even if you are certain you did it correctly.

Resources

• Algebra Help

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