One-Step & Two-Step Equations • Topic 1 of 1

Solving Two-Step Equations

Two-step equations require two inverse operations to isolate the variable. The general form is ax + b = c.

Steps to solve:

  1. Add or subtract to move the constant term to the other side
  2. Multiply or divide to isolate the variable
  3. Check by substituting your answer back into the original equation

Example: 2x + 3 = 11

Step 1: Subtract 3 from both sides: 2x = 8

Step 2: Divide both sides by 2: x = 4

Key rule: Whatever you do to one side, you must do to the other side.

EQUATION BALANCE SCALE:

   2x + 3  =  11
      |
  Subtract 3 from both sides
      |
    2x    =   8
      |
  Divide both sides by 2
      |
     x    =   4

VERIFY: 2(4) + 3 = 8 + 3 = 11 [correct!]
Solved Examples
1
Worked Example
Solve: 3x - 7 = 14
Solution3x - 7 + 7 = 14 + 7 => 3x = 21 => x = 7. Check: 3(7)-7 = 14. Correct!
2
Worked Example
Solve: x/4 + 2 = 10
Solutionx/4 + 2 - 2 = 10 - 2 => x/4 = 8 => x = 32. Check: 32/4+2 = 10. Correct!
3
Worked Example
Solve: -2x + 5 = 17
Solution-2x + 5 - 5 = 17 - 5 => -2x = 12 => x = -6. Check: -2(-6)+5 = 17. Correct!

Key Points

  • Always perform the same operation on BOTH sides
  • Undo addition/subtraction first, then multiplication/division
  • Check your answer by plugging it back into the original equation
  • Negative coefficients: dividing by a negative flips nothing (unlike inequalities)
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.To solve $2x+3=11$, first:
Explanation: Move the constant first.
Q2.The solution of $3x-7=14$ is:
Explanation: $3x=21\Rightarrow x=7$.
Q3.The solution of $2x+5=15$ is:
Explanation: $2x=10\Rightarrow x=5$.
Q4.You always check a solution by:
Explanation: Substitute back.
Practice more MCQs → 📝 Assignment · 35 marks