Solving One-Step Equations with Expressions
Grade 7 Mathematics Understanding algebraic expressions Mastering equation solving techniques
What Are Algebraic Expressions?
Combinations of numbers, variables, and operations Variables represent unknown values (like x or y) Examples: 3x, 2y + 5, 4a - 7 Building blocks for equations
From Expressions to Equations
An equation has two expressions separated by an equals sign Example: 3x + 5 = 14 The equals sign shows balance Our goal: find the value of the variable
Think About It
If x + 7 = 12, what operation would you use to find x? Remember: we want to get x by itself! What's the opposite of adding 7?
Inverse Operations: The Key to Solving
Addition ↔ Subtraction Multiplication ↔ Division Use inverse operations to isolate the variable What you do to one side, you must do to the other
Solving: x + 8 = 15
Step 1: Identify the operation (addition) Step 2: Use inverse operation (subtract 8) Step 3: x + 8 - 8 = 15 - 8 Step 4: x = 7 Step 5: Check by substituting back
Addition vs. Subtraction Equations
{"left":"x + 6 = 11\nSubtract 6 from both sides\nx = 5\nCheck: 5 + 6 = 11 ✓","right":"y - 4 = 9\nAdd 4 to both sides\ny = 13\nCheck: 13 - 4 = 9 ✓"}
Your Turn: Practice Problem
Solve: 3x = 21 What operation is being performed? What's the inverse operation? Show your work step by step Don't forget to check your answer!
Multiplication vs. Division Equations
{"left":"4x = 20\nDivide both sides by 4\nx = 5\nCheck: 4(5) = 20 ✓","right":"x ÷ 3 = 6\nMultiply both sides by 3\nx = 18\nCheck: 18 ÷ 3 = 6 ✓"}
Remember the Golden Rule
Whatever you do to one side of the equation, you must do to the other side to keep it balanced!