Solving One-Step Equations

Why This Matters for Nursing: "If a patient needs 250 mg and each tablet is 125 mg, how many tablets?" This is solving an equation: 125x = 250. Basic algebra helps you solve real medication problems.

What You Need to Know

An equation has an equals sign (=) showing two expressions are equal.

Solving means finding the value of the variable that makes the equation true.

The Golden Rule

Whatever you do to one side, you MUST do to the other side.

Think of a balanced scale—to keep it balanced, add/remove the same from both sides.

🧠 Memory Trick

"Undo the operation"

• If the variable is being ADDED to → SUBTRACT from both sides
• If the variable is being SUBTRACTED from → ADD to both sides
• If the variable is being MULTIPLIED → DIVIDE both sides
• If the variable is being DIVIDED → MULTIPLY both sides

Do the OPPOSITE (inverse operation)!

Four Types of One-Step Equations

Type 1: Addition Equation

x + 5 = 12 - Undo addition with subtraction - x + 5 - 5 = 12 - 5 - x = 7

Type 2: Subtraction Equation

x - 3 = 10 - Undo subtraction with addition - x - 3 + 3 = 10 + 3 - x = 13

Type 3: Multiplication Equation

4x = 20 - Undo multiplication with division - 4x ÷ 4 = 20 ÷ 4 - x = 5

Type 4: Division Equation

x/6 = 8 - Undo division with multiplication - (x/6) × 6 = 8 × 6 - x = 48

✏️ Worked Examples

Example 1: Addition Equation

Problem: n + 17 = 42

Step 1 — Identify the operation being done to the variable. The n is being added to 17. To undo addition, we subtract.

Step 2 — Do the opposite operation to BOTH sides. Subtract 17 from both sides: - Left side: n + 17 - 17 = n (the +17 and -17 cancel out, leaving just n) - Right side: 42 - 17 = 25

Step 3 — Write the answer. n = 25.

Step 4 — Check your answer. Plug 25 back in: 25 + 17 = 42. ✓

Answer: n = 25