Crack the Code: Challenging Two-Step Equations
Crack the Code: Challenging Two-Step Equations
Items in this lesson
Crack the Code: Challenging Two-Step Equations
What do you already know about solving two-step equations?
Learning Objective
At the end of the lesson you will confidently solve and explain hard two-step algebraic equations.
What Are Two-Step Equations?
A two-step equation is an equation that takes two operations to solve, like addition and division, or multiplication and subtraction.
Structure of Two-Step Equations
These equations often look like 3x + 7 = 19 or (x/2) – 4 = 6. You need to undo the operations in reverse order.
Order of Operations (Review)
Brackets, Indices, Division/Multiplication, Addition/Subtraction.
Solving Strategy
BIDMAS
Work backwards: undo addition/subtraction first, then multiplication/division.
Example 1
Solve: 3x + 7 = 19. Step 1: Subtract 7 from both sides. Step 2: Divide by 3.
Worked Example 1: Step-by-Step
Step 1: 3x + 7 = 19 aSubtract 7: 3x = 12 Step 2: Divide by 3: x = 4
Example 2
Solve: (x/4) - 5 = 2. Step 1: Add 5. Step 2: Multiply by 4.
Worked Example 2: Step-by-Step
Step 1: (x/4) - 5 = 2 aAdd 5: (x/4) = 7 Step 2: Multiply by 4: x = 28
How to Check Your Solution
Substitute your answer back into the original equation. If both sides are equal, your solution is correct.
Checking Example
Example: For x = 4 in 3x + 7 = 19, substitute 4: 3(4) + 7 = 19. Is it true? Yes!
Common Mistakes
1. Not undoing operations in reverse order. 2. Forgetting to do the same to both sides. 3. Arithmetic errors.
Harder Equations: Negative Numbers
Solve: 5x - 12 = -27. Carefully add 12 and then divide by 5. Watch the negatives!
Harder Equations: Fractions
Solve: (x/3) + 2 = -6. Subtract 2, then multiply by 3. Be careful with negatives and fractions.
Try It Yourself: Question 1
Solve: 2x - 9 = 7. Show your working.
Try It Yourself: Question 2
Solve: (x/5) + 3 = -1. Show your working.
Challenge Question 1
Solve: -4x + 8 = 0. Think carefully about negative numbers.
Challenge Question 2
Solve: (2x/3) - 9 = 13. Show all steps.
Tips for Solving Hard Equations
Check Answers
Substitute back into the original equation to confirm.
Write each step clearly. Double check your work.
Stay Organised
Reflect: What Did You Find Hard?
Think about the hardest equation. Was it fractions, negatives, or something else?
Next Steps
Practise more two-step equations with harder numbers. Remember your strategies!
Write down 3 things you learned in this lesson.
Write down 2 things you want to know more about.
Ask 1 question about something you haven't quite understood yet.
