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

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What is Solving a - x = b?

Grade Level:

Class 4

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

Definition

What is it?

Solving 'a - x = b' means finding the missing value of 'x' in an equation where a known number 'a' is reduced by 'x' to get another known number 'b'. It helps us figure out what number was subtracted.

Simple Example

Quick Example

Imagine you had 50 rupees (a) in your wallet. You bought some pakoras, and now you have 20 rupees (b) left. The equation would be 50 - x = 20. Solving for 'x' means finding out how much money (x) you spent on pakoras.

Worked Example

Step-by-Step

Let's solve the equation: 35 - x = 12

1. Our goal is to find the value of 'x'.
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2. We want to get 'x' by itself on one side of the equation. Currently, 'x' is being subtracted from 35.
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3. To move the 35 away from 'x', we can subtract 35 from both sides of the equation. Remember, whatever you do to one side, you must do to the other to keep it balanced.
35 - x - 35 = 12 - 35
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4. On the left side, 35 - 35 becomes 0, so we are left with -x.
-x = 12 - 35
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5. Now, calculate the right side: 12 - 35 = -23.
-x = -23
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6. We have -x = -23. To find 'x', we can multiply both sides by -1 (or simply change the sign on both sides).
(-1) * (-x) = (-1) * (-23)
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7. This gives us x = 23.

So, the solution is x = 23.

Why It Matters

Understanding how to solve these equations is fundamental to all STEM fields, from calculating distances in Physics to balancing chemical reactions. It's crucial for careers like engineering, data analysis, and even managing your personal finances, helping you make smart decisions about money and resources.

Common Mistakes

MISTAKE: Subtracting 'b' from 'a' directly when 'x' is negative, like in 'a - x = b' thinking x = a - b. | CORRECTION: Remember that 'x' is being subtracted. If you rearrange, it becomes a - b = x. So, x = a - b.

MISTAKE: Forgetting to change the sign of 'x' if you end up with -x = (some number). | CORRECTION: If you have -x = -5, then x must be 5. Always make 'x' positive by multiplying both sides by -1 if needed.

MISTAKE: Not performing the same operation on both sides of the equation. | CORRECTION: An equation is like a balance scale. Whatever you do to one side (add, subtract, multiply, divide), you MUST do to the other side to keep it balanced.

Practice Questions

Try It Yourself

QUESTION: Solve for x: 45 - x = 15 | ANSWER: x = 30

QUESTION: A farmer had 70 mangoes. After selling some (x), he had 28 mangoes left. Write an equation and solve for x. | ANSWER: 70 - x = 28; x = 42

QUESTION: If 120 - x = 50 + 10, what is the value of x? | ANSWER: 120 - x = 60; x = 60

MCQ

Quick Quiz

Which step is correct to solve 60 - x = 25 for x?

x = 60 + 25

x = 60 - 25

x = 25 - 60

-x = 60 + 25

The Correct Answer Is:

To isolate 'x', we can move 60 to the other side, making it -60. So, -x = 25 - 60, which means -x = -35. Therefore, x = 35. This is the same as directly calculating x = 60 - 25.

Real World Connection

In the Real World

This concept is used when managing your mobile data. If you start with 2 GB of data (a) and check later to see you have 0.5 GB left (b), you can use '2 - x = 0.5' to find out how much data (x) you've used. This helps you plan your usage better.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, usually with an equals sign (=) | VARIABLE: A letter (like 'x') that represents an unknown number in an equation | SOLVE: To find the value of the unknown variable that makes the equation true | BALANCE: Keeping both sides of an equation equal by performing the same operation on both sides.

What's Next

What to Learn Next

Great job understanding this! Next, you can learn about solving equations like 'a + x = b' and 'x - a = b'. These build on the same idea of balancing equations and will make you even better at finding missing numbers in different situations.