When you're learning to solve linear equations, one important skill is called "substituting back." This technique not only helps you check if your answer is right, but it also helps you understand the equation better.

Why is Substituting Back Important?

1. Checking Your Answers: After you figure out the value of a variable, it's important to put that value back into the original equation. This way, you can make sure your answer is correct.

   For example, if you solve the equation

   $2x + 3 = 11$

   and find that $x = 4$, you can check your answer by substituting back:

   $2(4) + 3 = 8 + 3 = 11.$

   Since both sides equal 11, you know that $x = 4$ is the right answer.

2. Building Confidence: When students substitute back and see that their answers work, it helps them feel more confident. They start to trust their methods and skills, which is really helpful during tests when you might feel nervous.

3. Understanding the Equation: Substituting back is a great way to learn more about how the numbers and variables in the equation relate to each other. By going back to the original equation with your answer, you're following the logic all the way through.

A Step-by-Step Example

Let’s solve this equation together:

$3x - 5 = 10.$

1. Isolate: First, add 5 to both sides. This gives you

   $3x = 15.$

2. Solve: Next, divide by 3 to find

   $x = 5.$

3. Substitute Back: Now, let’s put $5$ back into the original equation:

   $3(5) - 5 = 10.$

   If you simplify this, you get

   $15 - 5 = 10,$

   which shows that $x = 5$ is indeed the correct answer.

Conclusion

In short, substituting back is a very useful tool when you’re learning to solve linear equations. It helps you check your answers, builds your confidence, and deepens your understanding—all important for doing well on tests. So, make sure to practice this skill, and you’ll get better at solving these equations!