What is an Equation with one Variable?

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Grade Level:

Class 4

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

Definition

What is it?

An equation with one variable is like a balancing scale where both sides are equal. It has an unknown value, called a variable (usually shown as 'x'), and a '=' sign. Our goal is to find the value of this unknown variable that makes the equation true.

Simple Example

Quick Example

Imagine you have some ladoos (let's say 'x' ladoos) and your friend gives you 5 more. Now you have a total of 12 ladoos. We can write this as an equation: x + 5 = 12. Here, 'x' is the variable, and we need to find how many ladoos you had initially.

Worked Example

Step-by-Step

Let's solve the equation: x + 7 = 15
---Step 1: Our goal is to get 'x' by itself on one side of the equation. To do this, we need to remove the '+ 7' from the left side.
---Step 2: To remove '+ 7', we do the opposite operation, which is subtracting 7. We must do this on BOTH sides of the equation to keep it balanced.
x + 7 - 7 = 15 - 7
---Step 3: Simplify both sides.
x + 0 = 8
---Step 4: So, x = 8.
---Step 5: To check our answer, put x=8 back into the original equation: 8 + 7 = 15. Since 15 = 15, our answer is correct.
Answer: x = 8

Why It Matters

Equations with one variable are fundamental in almost all problem-solving! They help engineers design bridges, scientists understand nature, and even economists predict market trends. Learning this helps you build a strong foundation for careers in AI, data science, and even managing your own finances.

Common Mistakes

MISTAKE: Only performing an operation (like adding or subtracting) on one side of the equation. | CORRECTION: Always perform the same operation on BOTH sides of the '=' sign to keep the equation balanced.

MISTAKE: Confusing the variable 'x' with the multiplication sign 'x'. | CORRECTION: In equations, 'x' usually stands for an unknown number. When multiplying, we often use a dot (e.g., 3 . 5) or write the number next to the variable (e.g., 3x).

MISTAKE: Forgetting to check the answer by substituting the found value back into the original equation. | CORRECTION: Always substitute your answer back into the original equation to verify if both sides are equal. This confirms your solution is correct.

Practice Questions

Try It Yourself

QUESTION: If you spent Rs 20 on a packet of biscuits and now have Rs 30 left from your pocket money, how much money (let's call it 'm') did you have initially? Write and solve the equation. | ANSWER: m - 20 = 30; m = 50

QUESTION: Your favourite cricket team scored 'y' runs in the first innings. In the second innings, they scored 120 runs. If their total score for the match was 250 runs, what is 'y'? | ANSWER: y + 120 = 250; y = 130

QUESTION: A shopkeeper sold 'p' number of pens on Monday. On Tuesday, he sold double the number of pens he sold on Monday. If he sold a total of 45 pens over both days, how many pens ('p') did he sell on Monday? (Hint: First write an equation for total pens sold). | ANSWER: p + 2p = 45 => 3p = 45; p = 15

MCQ

Quick Quiz

Which of the following is an equation with one variable?

5 + 3 = 8

x + y = 10

7 - x = 2

2 < 5

The Correct Answer Is:

Option C (7 - x = 2) has an equals sign and only one unknown value ('x'), making it an equation with one variable. Option A is just an arithmetic statement. Option B has two variables (x and y). Option D is an inequality, not an equation.

Real World Connection

In the Real World

From calculating the best mobile data plan to figuring out how many ingredients you need for a recipe, equations are everywhere. For example, when a delivery app like Swiggy or Zomato calculates your estimated delivery time, it uses equations with variables like distance and traffic to give you an accurate prediction.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal, using an '=' sign. | VARIABLE: A symbol (usually a letter like 'x' or 'y') that represents an unknown number. | EXPRESSION: A combination of numbers, variables, and operation signs (like +, -, x, /) but no '=' sign. | SOLVE: To find the value of the variable that makes the equation true. | BALANCE: Keeping both sides of the equation equal by performing the same operation on both sides.

What's Next

What to Learn Next

Great job understanding equations with one variable! Next, you can explore 'Equations with Two Variables' or 'Solving Equations with Multiplication and Division'. These will build on what you've learned here and help you solve even more complex problems.