What is a one-step inequality?

A one-step inequality is an inequality that can be solved with just one operation — either:

• Addition

• Subtraction

• Multiplication

• Division

Think of it as the simplest type of inequality, just like one-step equations.

Goal: Solve for the variable in one step.

Symbols reminder

Step-by-step solving rules

1. Use inverse operations to isolate the variable

   • If a number is added → subtract it

   • If a number is subtracted → add it

   • If multiplied → divide

   • If divided → multiply

2. Important: If you multiply or divide by a negative number, flip the inequality sign.

Examples

Example 1: Addition

Step 1: Add 3 to both sides

✅ Solution: all numbers greater than 10

Example 2: Subtraction

Step 1: Subtract 5 from both sides

✅ Solution: all numbers less than or equal to 7

Example 3: Multiplication

Step 1: Divide both sides by 3

✅ Solution: all numbers less than 4

Example 4: Multiplying by a negative

Step 1: Divide both sides by −2 → flip inequality sign

✅ Solution: all numbers less than or equal to −4

Graphing one-step inequalities on a number line

• < or > → open circle

• ≤ or ≥ → closed circle

• Shade left for smaller numbers

• Shade right for larger numbers

Example: x > 10

• Open circle at 10

• Shade to the right

Common beginner mistakes

1. ❌ Forgetting to flip the inequality when multiplying/dividing by negative

2. ❌ Using a closed circle for < or >

3. ❌ Thinking there’s only one solution — inequalities often have many solutions

Why one-step inequalities matter

• They are the foundation for more complex inequalities

• Help you understand ranges of values

• Essential for word problems and graphing