Expressions & Equations: The Language of Algebra
Week 7 · Expressions & Equations
Learn to write and evaluate algebraic expressions, and solve one-step equations using inverse operations.
Variables and Expressions\nA **variable** is a letter that represents an unknown number (like x, y, or n).\nAn **expression** is a math phrase with numbers, variables, and operations.\n\n- "5 more than x" → x + 5\n- "3 times a number n" → 3n\n- "a number divided by 4" → n / 4\n\n## Evaluating Expressions\nSubstitute the value of the variable and calculate.\n\n**Evaluate 2x + 3 when x = 4:**\n- Replace x with 4: 2(4) + 3\n- Multiply first: 8 + 3\n- Add: **11**\n\n## Equations\nAn **equation** shows two expressions are equal: **3x = 15**\n\n## Solving One-Step Equations\nUse **inverse operations** (opposites) to isolate the variable.\n\n**x + 7 = 12** → Subtract 7 from both sides → x = 5\n**3x = 21** → Divide both sides by 3 → x = 7\n**x - 4 = 9** → Add 4 to both sides → x = 13\n**x / 4 = 6** → Multiply both sides by 4 → x = 24
Worked Examples
Example 1
📝 Evaluate 3m - 1 when m = 5.
✓ Answer: 14
Replace m with 5: 3(5) - 1 = 15 - 1 = 14.
Example 2
📝 Solve: 4x = 28.
✓ Answer: x = 7
Divide both sides by 4: 4x / 4 = 28 / 4, so x = 7.
Common Mistakes to Avoid
- ⚠️Performing the wrong inverse operation — if the equation adds, subtract; if it multiplies, divide
- ⚠️Only doing the operation to one side — whatever you do to one side, do to the other
- ⚠️Confusing an expression (no equals sign) with an equation (has an equals sign)