How Can We Check Our Answers to Linear Equations in Year 8 Math?

Checking answers to linear equations is an important skill in Year 8 Math. It helps make sure that the answers we find are not just possible, but also right. This means we need to plug our answers back into the original equations and see if both sides are equal.

What Are Linear Equations?

A linear equation is a type of equation where the highest power of the variable (like $x$) is 1. This means it doesn't have any squared numbers or higher. It usually looks like this:

$$ax + b = c$$

Here:

• $a$, $b$, and $c$ are just numbers.
• $x$ is the variable we’re trying to find.

In Year 8, you might see equations that use both positive and negative numbers, fractions, and decimals.

How to Check Your Answers

1. Solve the Equation: Start by finding the value of $x$ in the equation. For example, look at this equation:

   $$2x + 3 = 11$$

   To find $x$, first subtract 3 from both sides:

   $$2x = 8$$

   Then divide both sides by 2:

   $$x = 4$$

2. Plug It Back In: Now that you have $x$, you need to put that value back into the original equation to check your answer:

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

   This simplifies to:

   $$8 + 3 = 11$$

   Since both sides are the same, $x = 4$ is the correct answer.

3. Check Both Sides: You can use this method for different types of linear equations. Always check both sides after plugging the answer back in to make sure they match.

Why Checking Answers is Important

• Finding Mistakes: Checking your work helps spot any mistakes you might’ve made while solving. Research shows that about 30% of kids in the UK make simple errors when working with linear equations. Checking helps catch these errors.

• Understanding Concepts: When you check your work, you also strengthen your knowledge about how linear equations work. The UK Math Curriculum wants students to solve equations and also understand their reasons behind the solutions.

• Building Good Habits: Regularly checking your answers helps develop good math habits. It gives students a clear way to solve problems. Reports show that students who check their answers often score 15% higher on tests compared to those who don’t.

Example Problems

Let's look at some examples to see how checking works:

1. Problem: Solve and check the equation $3x - 5 = 16$.

   • Solution: Add 5 to both sides to get $3x = 21$.
   • Now divide by 3: $x = 7$.
   • Check: Put $x = 7$ back into the original equation: $3(7) - 5 = 16 \implies 21 - 5 = 16$, which is true.

2. Problem: Solve and check the equation $5x + 2 = 3x + 10$.

   • Solution: Rearranging gives $2x = 8$, so $x = 4$.
   • Check: Substitute $x = 4$: $5(4) + 2 = 3(4) + 10 \implies 20 + 2 = 12 + 10 \implies 22 = 22$, which is correct.

Conclusion

Checking answers to linear equations is a key skill in Year 8 math. It not only proves our answers are right but also helps us understand math better. By following a step-by-step way to solve and check equations, students prepare themselves for more advanced math as they continue learning.