Solving Equations with Addition and Subtraction

Video Lessons > Solving Equations with Addition and Subtraction

Introduction and Video

In this video lesson, we will learn the process of solving equations with addition and subtraction. We will go through some sample problems and also practice verifying our answers to ensure accuracy.

Overview of Solving Equations with Addition and Subtraction

Remember that the goal of solving any equation is to isolate the variable. That means getting the variable alone on one side of the variable. If there are other terms with the variable, we can undo them using opposite operations. If the equation shows a number being added to the variable, we can undo the number using subtraction. Similarly, if the equation shows a number being subtracted from the variable, we can undo it using addition.

Lesson Notes

Let's look at the steps for solving equations with addition and subtraction.

Example 1: Solving n + 9 = 15

Before solving, it's helpful to draw a line through the equal sign to distinguish the left and right sides of the equation. This helps with organization. Our goal is to isolate the variable, meaning it should only be on the left side with the number on the right side. To achieve this, we must eliminate the +9 on the left side.

• Undo: To undo the addition, we use the opposite operation, which is subtraction. It's important to remember that whatever we do to one side, we must do to the other to maintain balance, similar to a scale.
• Simplify: Simplifying both sides by combining like terms, we end up with n + 0 on the left and 6 on the right. Since adding zero does not change the value, we can simplify further to just n = 6. This is a solved equation with the variable on one side, the number on the other, and an equal sign in the middle.
• Check: To confirm our answer, we can check it by substituting 6 for n in the original equation and simplifying to get a true equation.

Example 2: Solving 12 = x - 8

Once again, we draw a line through the equal sign and follow the same steps as before. Even though the variable is on the right side, we can still solve the equation by isolating the variable.

• Undo and Simplify: By adding 8 to both sides, simplifying, and eliminating the plus zero, we end up with a solved equation of 20 = x.
• Check: Checking our answer by substituting 20 for x gives us a true equation, confirming that our answer is correct.

Summary and Practice

In this video lesson, we learned how to solve equations with addition and subtraction. We start by isolating the variable on one side and simplifying the equation. As long as we keep our work organized and follow each step carefully, we can successfully solve equations. And don't forget to double-check answers for accuracy.

Try this practice activity to see what you learned. Complete the steps of solving this equation by dragging each element on the right to its correct place.

Related Standard: Common Core 6.EE.B.7