⚖️ Solving Equations
Cambridge Lower Secondary · Grade 7 · Algebra
One-Step Equation
x + 5 = 12 → subtract 5 from both sides → x = 7 The balance stays level ⚖️
Two-Step Equation
2x + 3 = 11 → subtract 3 → 2x = 8 → divide by 2 → x = 4 Undo in reverse order
Variables on Both Sides
3x + 2 = x + 10 → collect x terms → 2x = 8 → x = 4 Move all x to one side first
Watch the balance in action! ⚖️
x + 5 = 12
▶ Subtract 5 from both sides
What you'll learn:
Solving one-step equations (add, subtract, multiply, divide)
Solving two-step equations in the correct order
Equations with the variable on both sides
Expanding brackets before solving
Forming equations from word problems
Checking solutions by substitution
📖 Learn: Solving Equations
Part 1: What is an Equation?
An equation is a mathematical statement that two expressions are equal . Think of it as a set of balance scales — whatever you do to one side, you must do to the other to keep them balanced.
⚖️ Golden Rule: Whatever you do to one side, do the same to the other side.
The solution is the value of the unknown (usually x) that makes the equation true.
💡 Check your answer by substituting back: if x = 7 in x + 5 = 12, then 7 + 5 = 12 ✓
Part 2: One-Step Equations
For one-step equations, apply a single inverse operation to isolate x.
➕ If the equation adds, you subtract : x + 5 = 12 → subtract 5 → x = 7
➖ If the equation subtracts, you add : x − 4 = 9 → add 4 → x = 13
✖️ If the equation multiplies, you divide : 3x = 21 → divide by 3 → x = 7
➗ If the equation divides, you multiply : x/4 = 7 → multiply by 4 → x = 28
💡 Inverse operations "undo" each other: + undoes −, × undoes ÷
Part 3: Two-Step Equations
Two-step equations need two inverse operations. Always undo addition/subtraction first , then multiplication/division.
Step 1: Undo the +/− (deal with the constant term)
Step 2: Undo the ×/÷ (deal with the coefficient of x)
Example: 2x + 3 = 11x = 4
Example: 5x − 4 = 16x = 4
Part 4: Variables on Both Sides
When x appears on both sides, collect all x terms on one side and all numbers on the other.
Step 1: Move all terms with x to one side (usually the side with more x)
Step 2: Move all number terms to the other side
Step 3: Solve the resulting one-step or two-step equation
Example: 3x + 2 = x + 10x = 4
💡 If you end up with something like 0 = 5, there is no solution. If 0 = 0, any x works!
Part 5: Equations with Brackets
When the equation contains brackets, expand first , then solve normally.
Step 1: Expand the bracket(s) by multiplying out
Step 2: Simplify by collecting like terms if needed
Step 3: Solve as a two-step equation
Example: 2(x + 3) = 14x = 3 x = 4
💡 Always substitute your answer back in to verify!
💡 Worked Examples
Example 1: One-Step Equation
Solve: x/4 = 7
🎯 Goal: get x on its own
x is being divided by 4, so the inverse is to multiply by 4
x/4 × 4 = 7 × 4
✅ x = 28
Check: 28 ÷ 4 = 7 ✓
Example 2: Two-Step Equation
Solve: 5x − 4 = 16
🎯 Undo subtraction first: add 4 to both sides
5x − 4 + 4 = 16 + 4 → 5x = 20
Now undo multiplication: divide both sides by 5
5x ÷ 5 = 20 ÷ 5 → ✅ x = 4
Check: 5(4) − 4 = 20 − 4 = 16 ✓
Example 3: Variables on Both Sides
Solve: 5x + 1 = 2x + 13
🎯 Collect x terms: subtract 2x from both sides
5x − 2x + 1 = 13 → 3x + 1 = 13
Subtract 1 from both sides: 3x = 12
Divide by 3: ✅ x = 4
Check: 5(4) + 1 = 21 and 2(4) + 13 = 21 ✓
Example 4: Brackets + Word Problem
"I think of a number, add 4, then multiply by 3. The result is 24. Find the number."
📝 Let the number be x. Write the equation: 3(x + 4) = 24
Expand: 3x + 12 = 24
Subtract 12: 3x = 12
Divide by 3: ✅ x = 4
Check: 3(4 + 4) = 3 × 8 = 24 ✓
⚖️ Balance Scales Visualizer
Apply operations to both sides. Keep the scales balanced to solve the equation!
Choose equation:
x + 5 = 12 (one-step)
3x = 21 (one-step ×)
2x + 3 = 11 (two-step)
3x + 2 = x + 10 (both sides)
2(x + 3) = 14 (brackets)
x + 5 = 12
⚖️ Balanced! Choose an operation to apply to both sides.
🔄 Reset
🔄 Reverse Flow: Function Machine
The machine applied operations to x to get the output. Click the inverse operations in the correct order (working backwards) to find x!
Choose puzzle:
Puzzle 1: ×3 then +4 → output 19
Puzzle 2: +6 then ×2 → output 20
Puzzle 3: ×4 then −3 → output 17
Puzzle 4: ÷2 then +5 → output 11
Now click the inverse operations in reverse order to find x:
Slots to fill (right to left — undo the last operation first):
🔄 Reset puzzle
🏗️ Equation Builder
Drag tiles into the drop zone to build the equation from the word problem, then solve it!
Loading...
Tile pool — click a tile to add it:
Your equation (click a placed tile to remove it):
Click tiles above to build your equation here
✅ Check equation
🗑️ Clear
➡️ Next problem
🪜 Step-by-Step Solver
Fill in each step to solve the equation. Choose the operation and value for each line!
Choose equation:
3x + 4 = 19
4x − 6 = 10
2(x + 5) = 18
6x + 1 = 3x + 13
✏️ Exercise 1: One-Step Equations
Solve each equation. Write the value of x.
✅ Check all answers
✏️ Exercise 2: Two-Step Equations
Solve each equation. Show your working mentally.
✅ Check all answers
✏️ Exercise 3: Variables on Both Sides
Collect all x terms on one side, then solve.
✅ Check all answers
✏️ Exercise 4: Equations with Brackets
Expand the brackets first, then solve.
✅ Check all answers
📝 Exercise 5: Form and Solve
Read each word problem. Write the equation then solve it.
✅ Check all answers
📝 Practice: 20 Questions
Mixed equations — click the correct answer for each question.
🏆 Challenge: 8 Questions
Harder equations and multi-step problems. Think carefully!