Master solving one-step equations using inverse operations with pizza party scenarios!
Scenario: You're planning a pizza party for your friends. You know that each pizza costs $12, and you have $60 to spend. How many pizzas can you buy?
An equation is a mathematical statement that shows two expressions are equal. It has an equals sign (=) and usually contains a variable that we need to find.
12x = 60
This means: 12 times some number equals 60
12 times the number of pizzas (x)
Total money available ($60)
Inverse operations are operations that "undo" each other. They help us solve equations by isolating the variable.
Addition ↔ Subtraction
Multiplication ↔ Division
If x + 5 = 12, then x = 12 - 5 = 7
If 3x = 15, then x = 15 ÷ 3 = 5
Let's solve 12x = 60 step by step:
12x = 60
Original equation
12x ÷ 12 = 60 ÷ 12
Divide both sides by 12 (inverse of multiplication)
x = 5
Solution: You can buy 5 pizzas!
Think of an equation like a balanced scale. Whatever you do to one side, you must do to the other side to keep it balanced.
Left side
Right side
Divided both sides by 12 to isolate x
Keeps the equation balanced and true
Movie tickets cost $8 each. You have $40. How many tickets can you buy?
8x = 40
Write the equation
x = 40 ÷ 8 = 5
Solve using inverse operations
Answer: You can buy 5 movie tickets.
Solve: x + 7 = 15
x = 15 - 7 = 8
Solve: 4x = 28
x = 28 ÷ 4 = 7
After solving an equation, always substitute your answer back into the original equation to make sure it's correct.
Original: 12x = 60
Our solution was x = 5
Check: 12(5) = 60
Substitute x = 5
60 = 60 ✓
Both sides are equal - our answer is correct!