What is Solving x - a = b? | Simple Explanation for Class 4

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What is Solving x - a = b?

Grade Level:

Class 4

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Definition

What is it?

Solving 'x - a = b' means finding the value of 'x' that makes the equation true. Here, 'x' is a mystery number, 'a' is a number you subtract from 'x', and 'b' is the result you get.

Simple Example

Quick Example

Imagine you had some ladoos (let's call this 'x'). You gave away 5 ladoos to your friend ('a' = 5). Now you have 7 ladoos left ('b' = 7). So, the equation is x - 5 = 7. Solving this means finding how many ladoos you started with.

Worked Example

Step-by-Step

Let's solve the equation: x - 12 = 25

Step 1: We want to find 'x'. Right now, 12 is being subtracted from 'x'.
---Step 2: To get 'x' alone, we need to do the opposite of subtracting 12. The opposite is adding 12.
---Step 3: Add 12 to BOTH sides of the equation to keep it balanced.
x - 12 + 12 = 25 + 12
---Step 4: On the left side, -12 + 12 becomes 0, leaving just 'x'.
x = 25 + 12
---Step 5: On the right side, add the numbers.
x = 37

So, the value of x is 37.

Why It Matters

Understanding how to solve equations like this is super important for many subjects! Scientists use it to calculate things in Physics and Chemistry, economists use it to understand money, and even computer programmers use it to write code. It's a basic building block for problem-solving in almost any career you can imagine, from a data scientist to an engineer.

Common Mistakes

MISTAKE: Subtracting 'a' from 'b' instead of adding. For x - 5 = 7, some might do 7 - 5 = 2. | CORRECTION: To undo subtraction, you must always add the number to the other side.

MISTAKE: Only adding 'a' to one side of the equation. For x - 10 = 20, they might write x = 20 + 10, but not add 10 to the left side in their head. | CORRECTION: Remember the 'balance' rule: whatever you do to one side of the '=' sign, you must do to the other side.

MISTAKE: Getting confused by larger numbers and making simple addition errors. For x - 35 = 68, they might miscalculate 68 + 35. | CORRECTION: Take your time with the addition. You can use mental math, count on your fingers, or write it down carefully to avoid errors.

Practice Questions

Try It Yourself

QUESTION: Solve for x: x - 8 = 15 | ANSWER: x = 23

QUESTION: Your dad had some money (x) in his wallet. He spent Rs. 150 on vegetables. Now he has Rs. 275 left. How much money did he have initially? (Write an equation and solve it) | ANSWER: x - 150 = 275, so x = 425. He had Rs. 425 initially.

QUESTION: If x - 48 = 93, what is the value of x? | ANSWER: x = 141

MCQ

Quick Quiz

What is the correct first step to solve x - 18 = 30?

Subtract 18 from 30

Add 18 to 30

Divide 30 by 18

Multiply 30 by 18

The Correct Answer Is:

To isolate 'x' when 18 is being subtracted, you perform the opposite operation, which is addition. So, you add 18 to both sides of the equation.

Real World Connection

In the Real World

Imagine you are tracking your daily steps using a fitness app. If the app shows you walked 'x' steps today, and you know you took 2000 steps in the morning, and the app's total is now 8000 steps, you can use 'x - 2000 = 8000' to figure out how many steps you walked after morning. This is how many apps calculate missing values or totals.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, usually with an '=' sign. | VARIABLE: A letter (like 'x') that represents an unknown number. | SOLVING: Finding the value of the unknown variable that makes the equation true. | INVERSE OPERATION: The operation that undoes another operation (e.g., addition is the inverse of subtraction).

What's Next

What to Learn Next

Great job learning about solving 'x - a = b'! Next, you should explore solving equations like 'x + a = b'. It uses similar ideas of balancing equations and inverse operations, which will make you even better at algebra!