What is Adding to Both Sides?

S1-SA5-0138

Grade Level:

Class 4

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

Definition

What is it?

Adding to both sides means performing the exact same addition operation on both sides of an equation. This keeps the equation balanced, like a perfectly balanced weighing scale, ensuring that both sides remain equal.

Simple Example

Quick Example

Imagine you have 5 laddoos on one plate and 5 laddoos on another plate. If you add 2 more laddoos to the first plate, you must also add 2 more laddoos to the second plate to keep them equal. Both plates will then have 7 laddoos.

Worked Example

Step-by-Step

Let's say we have the equation: x - 3 = 7. We want to find the value of x.

Step 1: The equation is x - 3 = 7.

---

Step 2: To get 'x' alone on one side, we need to remove the '-3'. The opposite of subtracting 3 is adding 3.

---

Step 3: Add 3 to the left side of the equation: (x - 3) + 3.

---

Step 4: To keep the equation balanced, we must also add 3 to the right side: 7 + 3.

---

Step 5: Now the equation looks like: x - 3 + 3 = 7 + 3.

---

Step 6: Simplify both sides: x = 10.

Answer: So, the value of x is 10.

Why It Matters

Understanding how to add to both sides is crucial for solving equations in all of mathematics and science. Engineers use it to design bridges, economists use it to model market trends, and data scientists use it to build predictive models. It's a foundational skill for problem-solving in fields like AI and Physics.

Common Mistakes

MISTAKE: Adding a different number to each side of the equation. | CORRECTION: Always add the exact same number to both the left and right sides to maintain balance.

MISTAKE: Adding to only one side of the equation. | CORRECTION: An equation is like a balance scale; whatever you do to one side, you must do to the other to keep it balanced.

MISTAKE: Adding when subtraction is needed to isolate the variable. | CORRECTION: Use the inverse operation. If a number is subtracted from the variable, add that number. If it's added, subtract it.

Practice Questions

Try It Yourself

QUESTION: Solve for y: y - 5 = 12 | ANSWER: y = 17

QUESTION: If a number decreased by 8 is 20, what is the number? | ANSWER: 28

QUESTION: Rahul had some cricket cards. He gave 6 away and now has 15. How many did he start with? Write an equation and solve it. | ANSWER: Let 'c' be the number of cards Rahul started with. Equation: c - 6 = 15. Solution: c = 21.

MCQ

Quick Quiz

What is the correct next step to solve the equation: x - 9 = 15?

Subtract 9 from both sides

Add 9 to the left side only

Add 9 to both sides

Multiply both sides by 9

The Correct Answer Is:

To isolate 'x', we need to undo the '-9'. The opposite of subtracting 9 is adding 9. To keep the equation balanced, we must add 9 to both sides. Options A, B, and D would unbalance or incorrectly solve the equation.

Real World Connection

In the Real World

When you manage your monthly mobile data, if you use 2 GB and want to know how much you started with, knowing you have 3 GB left, you'd use this concept. (Data used + Data remaining = Total data). Similarly, shopkeepers use this to calculate stock: (items sold + items remaining = initial stock).

Key Vocabulary

Key Terms

EQUATION: A statement that two mathematical expressions are equal | VARIABLE: A symbol, usually a letter, representing an unknown value | BALANCE: To keep both sides of an equation equal | INVERSE OPERATION: An operation that undoes another operation (e.g., addition undoes subtraction)

What's Next

What to Learn Next

Great job understanding adding to both sides! Next, you should learn about 'Subtracting from Both Sides'. It's the same idea but with subtraction, and it will further strengthen your equation-solving skills.