Master solving simple equations using balance scales and inverse operations. Learn equation solving through balance scale laboratory activities.
Scenario: You're in a balance scale laboratory! You have a balance scale with x + 3 on the left side and 7 on the right side. The scale is balanced, which means both sides are equal. You need to find the value of x that makes this true. What do you do?
This laboratory will teach you how to solve equations using the balance scale method - whatever you do to one side, you must do to the other to keep it balanced!
An equation is a mathematical statement that shows two expressions are equal. It has an equals sign (=) between them.
Think of an equation as a balanced scale. Whatever you do to one side, you must do to the other to keep it balanced.
Keep the equation balanced by doing the same operation to both sides
Look at what operation is being done to the variable. Is it addition, subtraction, multiplication, or division?
Example: x + 3 = 7 → addition is being done to x
To solve for the variable, use the inverse (opposite) operation. Do the same to both sides to keep the equation balanced.
Example: x + 3 = 7 → subtract 3 from both sides → x = 4
Substitute your answer back into the original equation to make sure it works.
Example: x = 4, so 4 + 3 = 7 ✓ (correct!)
Solve these equations using the balance scale method:
Write equations for these situations:
1. x + 4 = 9
2. y + 6 = 14
3. n + 8 = 15
4. a + 3 = 11
5. x - 2 = 7
6. y - 5 = 12
7. n - 3 = 9
8. a - 6 = 8
9. 2x = 10
10. 3y = 18
11. x ÷ 4 = 3
12. y ÷ 2 = 7
Wrong: x + 3 = 7 → x = 7 (only subtracted from left side)
Correct: x + 3 = 7 → x + 3 - 3 = 7 - 3 → x = 4
Wrong: Solving x + 3 = 7 and getting x = 4, but not checking
Correct: Always check: 4 + 3 = 7 ✓
Equations show that two expressions are equal
Use inverse operations to solve for the variable
Always do the same operation to both sides
Check your answer by substituting it back into the original equation