← Pre-Algebra

Unit 6: Inequalities

What changes — and what famously flips — when an equation's equals sign becomes greater than or less than.

5 topics · 18 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

What an Inequality Means

  1. How it worksHow does an inequality describe a whole range of numbers instead of just one?
  2. Worked exampleShow me the inequality for a ride that requires a height of at least 48 inches.
  3. Going furtherWhat happens to the solution set when you change greater than to greater than or equal to?
  4. Common mistakeWhy doesn't x is greater than 5 include the number 5 itself?
Your turn1 of 2
A ride requires a height of at least 53 inches. Which inequality describes the allowed heights h?

Solving One-Step and Two-Step Inequalities

  1. How it worksHow do you isolate the variable in an inequality using the same undo-moves as an equation?
  2. Worked exampleSolve x plus 3 is greater than 10 for x.
  3. Worked exampleSolve 2x minus 5 is less than or equal to 9 for x.
Your turn1 of 2
Ravi needs to save more than 42 dollars in total. He already has x dollars plus 14 more in birthday money. Solve x plus 14 is greater than 42 to find the boundary value of x.

Why Multiplying or Dividing by a Negative Flips an Inequality

  1. How it worksHow does multiplying by a negative number swap the positions of two points on the number line, forcing the inequality sign to flip?
  2. Worked exampleSolve negative 3x plus 4 is greater than 19 for x, flipping the sign at the right step.
  3. Common mistakeWhy doesn't the inequality sign flip when you add or subtract a negative number instead of multiplying or dividing by one?
  4. Going furtherWhat happens to the flip rule when you multiply both sides of an inequality by a negative fraction?
Your turn1 of 2
A tank starts with 15 litres and drains at negative 7x litres, where x is the number of minutes, and must stay above 37 litres. Solve negative 7x plus 15 is greater than 37 to find the boundary value of x.

Graphing Inequalities on a Number Line

  1. How it worksHow does an open or closed circle plus a shaded arrow show every number that makes an inequality true?
  2. Worked exampleGraph the solution to x is less than or equal to negative 2 on a number line.
  3. Common mistakeWhy doesn't the shaded arrow in a number line graph ever point in both directions at once for a simple inequality?
  4. Going furtherWhat happens to a number line graph when it has to show x is greater than negative 2 and less than 5 at the same time?
Your turn1 of 2
You graph x is greater than 14 on a number line. Should the circle at 14 be open or filled in (closed)?

Writing an Inequality from a Real Situation

  1. How it worksHow do you translate a real limit, like a weight limit or a minimum age, into an inequality with a variable?
  2. Worked exampleFind the gigabytes allowed by an inequality for a plan costing 15 dollars plus 3 dollars per gigabyte, total under 30 dollars.
  3. Ties togetherHow does turning a real limit into an inequality reuse the setup-fee-and-rate translation from equation word problems?
Your turn1 of 2
Zoe's phone plan costs 15 dollars plus 4 dollars per gigabyte, and her budget is under 95 dollars. How many gigabytes, at most, can she use?