Solving Multi-Step Equations

Why This Matters for Nursing: Real-world calculations often have multiple steps. "A patient receives a loading dose plus hourly maintenance: Loading + 2(hourly) = Total." Multi-step equations help you work backward to find missing values.

What You Need to Know

Multi-step equations require more than one operation to solve. The key is working in the right ORDER:

The Strategy (Reverse PEMDAS!)

1. Simplify each side first (distribute, combine like terms)
2. Move variables to one side (add/subtract terms with variables)
3. Undo addition/subtraction (isolate the term with the variable)
4. Undo multiplication/division (isolate the variable)

🧠 Memory Trick

"Undo in reverse order"

If the equation was built by multiplying then adding, UNDO by subtracting then dividing.

Think: Getting dressed vs. undressing — you put on socks then shoes, but take off shoes then socks!

Step-by-Step Process

Example: Solve 3x + 5 = 20

1. Undo addition: Subtract 5 from both sides
2. 3x + 5 - 5 = 20 - 5

3. 3x = 15

4. Undo multiplication: Divide both sides by 3

5. 3x ÷ 3 = 15 ÷ 3

6. x = 5

7. Check: 3(5) + 5 = 15 + 5 = 20 ✓

✏️ Worked Examples

Example 1: Two Operations

Problem: 2x - 7 = 15

Step 1 — Undo addition/subtraction first. The 7 is being subtracted from the 2x side. To undo it, add 7 to both sides. - Left: 2x - 7 + 7 = 2x - Right: 15 + 7 = 22 - Now we have: 2x = 22

Step 2 — Undo multiplication. The x is multiplied by 2. Divide both sides by 2. - x = 22 ÷ 2 = 11

Step 3 — Check. Plug back in: 2(11) - 7 = 22 - 7 = 15. ✓

Answer: x = 11