Solving Two-Step Equations

This lesson teaches how to isolate a variable using inverse operations. The main idea is to treat an equation like a balance scale: whatever you do to one side, you must do to the other side. Students use addition, subtraction, multiplication, and division to undo operations step by step until the variable stands alone.

For example, in an equation such as -16 = x/4 + 2, first subtract 2 to isolate the variable term, giving -18 = x/4. Then multiply both sides by 4 to undo the division and get x = -72. Checking the solution by substitution confirms the answer.

By the end of the lesson, students should be able to recognize the order of inverse operations, solve two-step equations accurately, and explain why equal changes must be made on both sides of an equation.

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Step-by-step example: solve for x in -16 = x/4 + 2

  1. Write the original equation: −16 = x/4 + 2
  2. Subtract 2 from both sides (undo the addition): −16 − 2 = x/4 + 2 − 2 −18 = x/4
  3. Multiply both sides by 4 (undo the division): −18 × 4 = (x/4) × 4 −72 = x
  4. Write the solution: x = −72
  5. Check by substituting back: −16 = (−72)/4 + 2 −16 = −18 + 2 −16 = −16 ✓