What is a Value that Makes an Equation True?

S1-SA5-0290

Grade Level:

Class 5

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

Definition

What is it?

A 'value that makes an equation true' is the specific number that, when placed into an equation, makes both sides of the equals sign perfectly balanced. It's like finding the missing piece that makes the math puzzle correct. This special number is also called the 'solution' to the equation.

Simple Example

Quick Example

Imagine you have a small box of ladoos, and your friend gives you 3 more. Now you have a total of 10 ladoos. If 'x' is the number of ladoos you had in the box initially, the equation is x + 3 = 10. The value that makes this equation true is 7, because 7 + 3 = 10. So, you started with 7 ladoos.

Worked Example

Step-by-Step

Let's find the value of 'y' that makes the equation y - 5 = 12 true.

Step 1: Write down the equation: y - 5 = 12
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Step 2: We want to get 'y' by itself on one side. To do this, we need to undo the '- 5'. The opposite of subtracting 5 is adding 5.
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Step 3: Add 5 to BOTH sides of the equation to keep it balanced: y - 5 + 5 = 12 + 5
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Step 4: Simplify both sides: y = 17
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Step 5: Check if this value makes the original equation true: 17 - 5 = 12
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Step 6: Yes, 12 = 12. The equation is true.

Answer: The value of y that makes the equation true is 17.

Why It Matters

Understanding how to find these values is super important! It's the basic building block for solving problems in science, engineering, and even finance. Scientists use it to predict outcomes, engineers to design structures, and economists to understand market trends. It's key for careers in AI, data science, and even managing your pocket money!

Common Mistakes

MISTAKE: Adding or subtracting only from one side of the equation. For example, in x + 5 = 10, subtracting 5 only from the left side (x = 10) | CORRECTION: Whatever you do to one side of the equals sign, you MUST do the exact same thing to the other side to keep the equation balanced. So, x + 5 - 5 = 10 - 5.

MISTAKE: Confusing the operation. For example, in 3x = 15, students might subtract 3 instead of dividing by 3. | CORRECTION: Always use the inverse (opposite) operation. If a number is added, subtract it. If multiplied, divide. If subtracted, add. If divided, multiply.

MISTAKE: Not checking the answer. Students find a value but don't substitute it back into the original equation. | CORRECTION: Always substitute your found value back into the original equation to verify if both sides are equal. This confirms your solution is correct.

Practice Questions

Try It Yourself

QUESTION: What value of 'p' makes the equation p + 8 = 15 true? | ANSWER: p = 7

QUESTION: Find the value of 'k' that makes 4k = 28 true. | ANSWER: k = 7

QUESTION: If a shopkeeper sold 12 mangoes and still has 'm' mangoes left, and he started with a total of 30 mangoes, what value of 'm' makes the equation m + 12 = 30 true? | ANSWER: m = 18

MCQ

Quick Quiz

For the equation 7 - x = 2, what value of 'x' makes the equation true?

-5

The Correct Answer Is:

If x = 5, then 7 - 5 = 2, which is true. Options A, C, and D do not make the equation true when substituted for x.

Real World Connection

In the Real World

When you use a ride-sharing app like Ola or Uber, the app calculates the fare based on distance and time. If your ride cost Rs. 150 and the base fare was Rs. 30, the app solves an equation like 'distance_cost + 30 = 150' to figure out how much the distance part added. Similarly, when you calculate your monthly mobile data usage, you might use equations to see how much data you have left.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal | VARIABLE: A letter (like x, y) that represents an unknown number | SOLUTION: The value of the variable that makes an equation true | BALANCE: Keeping both sides of an equation equal by doing the same operation to both sides

What's Next

What to Learn Next

Great job understanding this core idea! Next, you can learn about solving equations with more than one step, or equations involving multiplication and division. These next steps will build on what you've learned here, helping you solve even trickier real-world math problems!