What is Solving x + a = b?

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Grade Level:

Class 4

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

Definition

What is it?

Solving x + a = b means finding the hidden value of 'x' in an equation. It's like a puzzle where you need to figure out the missing number that makes both sides of the equation equal.

Simple Example

Quick Example

Imagine you bought some samosas for Rs. 20 and a chai. The total bill was Rs. 35. If we write this as 20 + x = 35, 'x' is the price of the chai. Solving this equation means finding out how much the chai cost.

Worked Example

Step-by-Step

Let's solve the equation: x + 10 = 25

Step 1: Our goal is to get 'x' by itself on one side of the equation.
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Step 2: To remove '+ 10' from the left side, we do the opposite operation, which is subtracting 10.
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Step 3: Remember, whatever you do to one side of the equation, you must do to the other side to keep it balanced. So, subtract 10 from both sides.
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x + 10 - 10 = 25 - 10
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Step 4: Simplify both sides.
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x = 15
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Step 5: Check your answer: Put 15 back into the original equation: 15 + 10 = 25. This is true!
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Answer: x = 15

Why It Matters

Understanding how to solve equations is super important! It's the base for all advanced maths, science, and even computer programming. Engineers use it to design bridges, economists use it to understand market prices, and even data scientists use it to make predictions.

Common Mistakes

MISTAKE: Only doing an operation (like subtracting a number) to one side of the equation. | CORRECTION: Always do the exact same operation to BOTH sides of the equation to keep it balanced.

MISTAKE: Confusing addition with subtraction when moving numbers. For example, trying to add 'a' when 'a' is already being added. | CORRECTION: To move a number to the other side, always do the OPPOSITE operation. If it's '+a', you subtract 'a'.

MISTAKE: Not simplifying the numbers after performing the operation. | CORRECTION: After you add or subtract from both sides, always do the calculation to find the new simplified numbers.

Practice Questions

Try It Yourself

QUESTION: Solve: y + 7 = 15 | ANSWER: y = 8

QUESTION: My friend gave me some cricket cards. I already had 12. Now I have 20 cards. How many did my friend give me? (Write as an equation and solve) | ANSWER: Equation: 12 + x = 20; x = 8

QUESTION: If a + 18 = 40, and b + 5 = 10, find the value of a + b. | ANSWER: a = 22, b = 5, so a + b = 27

MCQ

Quick Quiz

What is the value of 'p' in the equation: p + 9 = 21?

The Correct Answer Is:

To solve p + 9 = 21, subtract 9 from both sides: p + 9 - 9 = 21 - 9, which gives p = 12. Options A, C, D are incorrect calculations.

Real World Connection

In the Real World

When you use a calculator app to split a restaurant bill with friends, and you know the total and how much everyone else paid, you can use this type of equation to find out how much you owe! Or when a shopkeeper calculates change, they're mentally solving a similar equation.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, usually with an '=' sign. | VARIABLE: A letter (like x, y, a) that stands for an unknown number. | SOLVE: To find the value of the unknown variable in an equation. | 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 basic step! Next, you can learn about solving equations with subtraction (like x - a = b) and then equations involving multiplication and division. These build on the same idea of balancing equations!