What is a Value that Satisfies an Equation?

S1-SA5-0291

Grade Level:

Class 5

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

Definition

What is it?

A 'value that satisfies an equation' is a number that, when put in place of a variable (like 'x' or 'y'), makes both sides of the equation equal. It's like finding the missing piece that balances a weighing scale.

Simple Example

Quick Example

Imagine you have a box of laddoos, and you want to share them equally. If you have 'x' laddoos and you eat 2, then 8 laddoos are left. The equation is x - 2 = 8. The value that satisfies this equation is the number of laddoos you started with.

Worked Example

Step-by-Step

Let's find the value that satisfies the equation: x + 5 = 12.

1. Our goal is to get 'x' by itself on one side of the equals sign.
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2. To remove '+ 5' from the left side, we do the opposite operation: subtract 5.
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3. Whatever we do to one side of the equation, we must do to the other side to keep it balanced. So, subtract 5 from both sides:
x + 5 - 5 = 12 - 5
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4. Simplify both sides:
x + 0 = 7
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5. So, x = 7.
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6. To check, replace 'x' with 7 in the original equation: 7 + 5 = 12. Since 12 = 12, the value 7 satisfies the equation.

Answer: x = 7

Why It Matters

Understanding how to find values that satisfy equations is super important for solving problems in science, engineering, and even daily life. Scientists use this to predict weather, engineers use it to design bridges, and economists use it to understand market trends. It's the building block for many exciting careers!

Common Mistakes

MISTAKE: Only performing an operation on one side of the equation (e.g., adding 3 to the left side but not the right side). | CORRECTION: Always perform the same operation (addition, subtraction, multiplication, division) on BOTH sides of the equation to keep it balanced.

MISTAKE: Using the wrong inverse operation (e.g., adding to undo multiplication). | CORRECTION: To undo addition, subtract. To undo subtraction, add. To undo multiplication, divide. To undo division, multiply.

MISTAKE: Confusing the variable with a known number. | CORRECTION: Remember the variable (like 'x') is the unknown quantity you need to find. The known numbers help you find it.

Practice Questions

Try It Yourself

QUESTION: What value of 'y' satisfies the equation: y - 7 = 10? | ANSWER: y = 17

QUESTION: Find the value of 'a' that satisfies: 3 * a = 21. | ANSWER: a = 7

QUESTION: If you buy 4 packets of biscuits and pay Rs. 50, and you get Rs. 10 change, what is the cost of one packet (let 'c' be the cost of one packet)? The equation is 4c + 10 = 50. Find 'c'. | ANSWER: c = 10 (Each packet costs Rs. 10)

MCQ

Quick Quiz

Which value of 'p' satisfies the equation: p + 8 = 15?

The Correct Answer Is:

To find 'p', subtract 8 from both sides: p + 8 - 8 = 15 - 8, which gives p = 7. If you substitute 7 for p, 7 + 8 = 15, which is correct.

Real World Connection

In the Real World

Imagine you're tracking your mobile data usage. If you started with 'D' GB of data, used 2 GB, and now have 5 GB left, the equation is D - 2 = 5. Finding the value of 'D' tells you how much data you started with, helping you manage your phone plan. This is used by mobile companies and even you to check your data balance on apps like MyJio or Airtel Thanks.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, usually with an equals sign (=) | VARIABLE: A symbol (like x, y, a) that represents an unknown number | SATISFIES: Makes the equation true or balanced | INVERSE OPERATION: An operation that undoes another (e.g., addition undoes subtraction)

What's Next

What to Learn Next

Great job understanding this! Next, you should explore 'Solving One-Step Equations' and 'Solving Two-Step Equations'. These concepts will build directly on what you've learned here, helping you solve even more complex problems easily.