Crack the Code: Challenging Two-Step Equations

• newEditor
• Mathematics
• Lower Secondary (Key Stage 3)

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.