The lesson
Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
Reading inequality symbols
An inequality compares values that are not necessarily equal: < (less than), > (greater than), ≤ (at most), ≥ (at least). "At most 9" means x ≤ 9; "fewer than 5" means x < 5.
Solving and graphing
Solve an inequality the same way you solve an equation. Then graph the solution on a number line: an open circle for < or >, a closed (filled) circle for ≤ or ≥.
Solve and graph x + 3 < 10
- 1Subtract 3 from both sides: x < 7.
- 2Graph an open circle at 7 and shade everything to the left.
Why this matters
Solve like equations, then graph every value that works.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Doing different operations to each side of an equation. Whatever you add, subtract, multiply, or divide on one side, do to the other.
Combining unlike terms (like 3x and 4) as if they were the same kind of term.
Key ideas from this lesson
- Reading inequality symbols
- Solving and graphing
Video walkthroughs
Intro to Inequalities
Symbols like < and ≥ and what they mean on a number line.
Watch on YouTube
Solving Inequalities
Solve inequality problems the same way you solve equations.
Watch on YouTube
Inequalities on a Number Line
Graph simple inequalities with open or closed circles.
Watch on YouTube
Multi-Step Inequalities
Solve inequalities and know when to reverse the inequality sign.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfSolve: x + 4 > 11. Write the solution as an inequality.
Step-by-step solution
- 1Subtract 4 from both sides.
- 2x > 7.
Exercise 2
Try it yourselfWhich inequality means "x is at least 12"?
Step-by-step solution
- 1"At least" includes 12 and all greater values.
- 2That is x ≥ 12.
Exercise 3
Try it yourselfSolve: 3n ≤ 18.
Step-by-step solution
- 1Divide both sides by 3.
- 2n ≤ 6.
Exercise 4
Try it yourselfYou must be at least 48 inches tall to ride. Write an inequality for height h.
Step-by-step solution
- 1Height must be 48 or more.
- 2h ≥ 48.
Exercise 5
Try it yourselfSolve: 2x − 5 < 13.
Step-by-step solution
- 1Add 5 to both sides: 2x < 18.
- 2Divide by 2: x < 9.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Inequalities & Number Lines
Question 1 of 5
Which inequality represents 'x is at most 9'?