What is Checking the Solution of an Equation?

S1-SA5-0292

Grade Level:

Class 5

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

Checking the solution of an equation means putting the value you found for the unknown variable back into the original equation. You do this to see if both sides of the equation become equal. If they are equal, your solution is correct!

Simple Example

Quick Example

Imagine you bought 3 samosas and paid 60 rupees. If someone asks, 'How much does one samosa cost?', you might guess 20 rupees. To check, you'd say: 3 samosas * 20 rupees/samosa = 60 rupees. Since 60 = 60, your guess of 20 rupees is correct!

Worked Example

Step-by-Step

Let's check if x = 7 is the correct solution for the equation: x + 5 = 12

Step 1: Write down the original equation: x + 5 = 12

---Step 2: Substitute the value of x (which is 7) into the equation: 7 + 5 = 12

---Step 3: Calculate the left side of the equation: 7 + 5 = 12

---Step 4: Compare the left side with the right side: 12 = 12

---Step 5: Since both sides are equal, the solution x = 7 is correct!

Why It Matters

Checking solutions is like double-checking your work, ensuring accuracy in everything from calculating your monthly budget to designing a rocket. Engineers, scientists, and even financial analysts use this skill daily to make sure their calculations are flawless and reliable, preventing costly mistakes.

Common Mistakes

MISTAKE: Only checking one side of the equation after substituting the value. | CORRECTION: Always calculate both the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation separately and then compare them.

MISTAKE: Making calculation errors while substituting the value. | CORRECTION: Be very careful with addition, subtraction, multiplication, and division when you put the number back into the equation. Double-check your basic arithmetic.

MISTAKE: Not writing down the original equation before substituting. | CORRECTION: Always start by clearly writing the original equation. This helps you avoid errors and keeps your work organised.

Practice Questions

Try It Yourself

QUESTION: Is y = 4 the correct solution for the equation y - 2 = 6? | ANSWER: No

QUESTION: Check if a = 3 is the correct solution for the equation 2a + 5 = 11. | ANSWER: Yes

QUESTION: For the equation 3m - 7 = 8, if you found m = 5, show how you would check your answer. | ANSWER: Substitute m=5 into 3m - 7 = 8. This gives 3(5) - 7 = 8. So, 15 - 7 = 8. Which means 8 = 8. Yes, m=5 is correct.

MCQ

Quick Quiz

What is the main purpose of checking the solution of an equation?

To make the equation longer

To confirm if the value found makes both sides of the equation equal

To find a new solution

To change the original equation

The Correct Answer Is:

The main purpose is to verify if the solution you found is indeed correct by seeing if it balances the equation. Options A, C, and D describe actions that are not the goal of checking a solution.

Real World Connection

In the Real World

When a railway engineer calculates how much fuel a train needs for a journey, they use equations. After finding the amount, they 'check the solution' by plugging the value back into their calculations to ensure it matches the required distance and load. This prevents the train from running out of fuel mid-journey!

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing that two expressions are equal, usually with an equals sign (=) | SOLUTION: The value of the unknown variable that makes an equation true | SUBSTITUTE: To replace a variable with a specific number | VARIABLE: A letter (like x or y) that represents an unknown number in an equation | LEFT HAND SIDE (LHS): The expression on the left side of the equals sign in an equation

What's Next

What to Learn Next

Great job learning to check solutions! Next, you can explore 'Solving Simple Linear Equations' where you'll learn different methods to find these solutions yourself. This skill of checking will be super useful to confirm your answers every time!