What is Solving a * x = b?

S1-SA5-0237

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 value of 'x' that makes the equation true. Here, 'a' and 'b' are known numbers, and 'x' is the unknown number we need to find. It's like a puzzle where you figure out the missing piece.

Simple Example

Quick Example

Imagine you bought 3 packets of biscuits, and the total bill was 60 rupees. If each packet costs the same, how much does one packet cost? This can be written as 3 * x = 60, where 'x' is the cost of one packet.

Worked Example

Step-by-Step

Let's solve: 5 * x = 30

1. Our goal is to find the value of 'x'.
---2. To get 'x' by itself, we need to remove the '5' that is multiplying it.
---3. We do the opposite operation: division. We divide both sides of the equation by 5.
---4. (5 * x) / 5 = 30 / 5
---5. This simplifies to x = 6.
---6. To check, replace 'x' with 6 in the original equation: 5 * 6 = 30. Since 30 = 30, our answer is correct.

Answer: x = 6

Why It Matters

Solving equations like this helps us find unknown values in many real-life situations. From calculating how much paint you need for your room to understanding how much interest your bank savings earn, it's a fundamental skill. Engineers, scientists, and even business owners use this daily to make important decisions.

Common Mistakes

MISTAKE: Adding or subtracting 'a' from both sides instead of dividing | CORRECTION: Remember that 'a' is multiplying 'x', so to isolate 'x', you must perform the inverse operation, which is division.

MISTAKE: Only dividing one side of the equation by 'a' | CORRECTION: Whatever operation you do to one side of the equation, you MUST do the exact same operation to the other side to keep the equation balanced.

MISTAKE: Getting confused by decimals or fractions for 'a' or 'b' | CORRECTION: The method remains the same: divide 'b' by 'a'. Use your knowledge of decimal or fraction division carefully.

Practice Questions

Try It Yourself

QUESTION: Solve for x: 4 * x = 24 | ANSWER: x = 6

QUESTION: A car travels 80 km in 2 hours. If it travels at a constant speed (speed * time = distance), what is its speed? (Hint: 2 * x = 80) | ANSWER: x = 40 km/hr

QUESTION: If 7 * x = 49, and then (x + 3) * y = 50, find the value of y. | ANSWER: First, x = 7. Then (7 + 3) * y = 50, which means 10 * y = 50. So, y = 5.

MCQ

Quick Quiz

What is the first step to solve 6 * x = 42?

Add 6 to both sides

Subtract 6 from both sides

Divide both sides by 6

Multiply both sides by 6

The Correct Answer Is:

To isolate 'x', we must perform the inverse operation of multiplication, which is division. We divide both sides by 6 to keep the equation balanced.

Real World Connection

In the Real World

When you buy groceries using a payment app like Google Pay or PhonePe, the app calculates your total bill (b) based on the number of items (a) and the price of each item (x). If you know the total bill and the number of items, you can find the price of one item using a * x = b. This math helps apps work smoothly for millions of users every day!

Key Vocabulary

Key Terms

EQUATION: A statement that two mathematical expressions are equal | UNKNOWN: A value that is not yet known, usually represented by a letter like 'x' | INVERSE OPERATION: An operation that undoes another operation (e.g., division is the inverse of multiplication) | ISOLATE: To get a variable by itself on one side of an equation

What's Next

What to Learn Next

Great job understanding this! Next, you can learn about solving equations with addition and subtraction, like 'x + a = b' or 'x - a = b'. These build on the same idea of using inverse operations to find the unknown 'x'.