Solving One-Step Equations

Solving one-step equations is truly your “first step” in the world of solving linear equations. If you can solve one-step equations that means you will be prepared to handle the challenge of more complex equations such as two-step and multi-step equations. Believe me, it is not difficult. Once you mastered this particular skill, you will open yourself up to many possibilities.

In this lesson, we are going to cover five (5)  types or cases of one-step equations based on how they are solved. However, the fifth type is really the mixture or combination of the multiplication and division performed as one operation. This is really an important case because others may consider it as a two-step equation problem but in fact, it can be solved with a single step.

Five (5) Cases of Solving One-Step Equations

Case 1: Equations that are solvable by adding the same number to both sides of the equation.

Case 2: Equations that are solvable by subtracting the same number to both sides of the equation.

Case 3: Equations that are solvable by multiplying the same number to both sides of the equation.

Case 4: Equations that are solvable by dividing the same number to both sides of the equation.

Case 5: Equations that are solvable by multiplying the reciprocal of the coefficient of the term with a variable to both sides of the equation.


What does it mean to solve an equation?

Here’s a simple answer. If you can isolate or keep the variable by itself on one side of the equation (the left side or right side) such that the variable or letter has a coefficient of +1 while the constant or number is on the opposite side, then you have just solved the equation in question.


Examples of How to Solve One-Step Equations

Example 1: Solve the one-step equation.

x-3=9

Observe that the left side of the equation contains the variable x which is being subtracted by 3 while the right side contains the number positive nine, +9. Since the variable is already on the left side, let’s just keep it there.

However, to isolate the variable x, we have to get rid of -3. We can eliminate -3 by adding its opposite which is +3. To keep the equation balanced, we must also add +3 on the right side of the equation.

To reiterate, this is Case 1 of solving one-step equations because we added the same number to both sides of the equation.

x-3=9 → x-3+3=9+3 → x=12

Example 2: Solve the one-step equation.

12=y+7

This one-step linear equation is a bit different as compared to the first example. Notice that the variable is located on the right side of the equation. Don’t be bothered by it because it is not a big deal. 🙂

Remember that when solving an equation, you may keep the variable on either side of the equation. As long as in the end, the variable that you are solving is isolated on one side with a coefficient of +1. Therefore for this equation, it is convenient to keep the variable on the right side.

It is easy to see that subtracting both sides of the equation by 7 will do the “trick” because it will get rid of the +7 thereby isolating the variable y on the right side.

This is Case 2 since we subtracted the equation on both sides by the same number to solve it.

12=y+7 → 12-7=y+7-7 → 5=y

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