Virginia SOL Math / Grade 6 / Patterns, Functions & Algebra

6.PFA.4

One-Variable Inequalities

What you'll learn

  • Represent a situation with a one-variable inequality
  • Graph the solutions of an inequality on a number line
  • Identify values that make an inequality true

Words to know

Inequality —
a math sentence using >, <, greater than or equal to, or less than or equal to
Solution set —
all values that make an inequality true
At least —
greater than or equal to
At most —
less than or equal to
Number line —
a line that shows numbers in order

Why it matters Inequalities describe limits and ranges, like a minimum age, a speed limit, or a budget you must stay under.

Worked examples

Model ItI do

Is x = 5 a solution of x > 3?

Substitute 5 for x: is 5 greater than 3? Yes, so x = 5 is a solution of x > 3.

Try It TogetherWe do

Write an inequality for: a rider must be at least 48 inches tall.

At least means greater than or equal to. Letting h be the height, the inequality is h greater than or equal to 48.

Now YouYou do

Is x = 2 a solution of x < 2?

Substitute 2 for x and check whether the statement is true. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Is x = 5 a solution of x > 2? Yes or no.

  2. 2.Is x = 1 a solution of x < 1? Yes or no.

  3. 3.Write an inequality for: a number is greater than 10.

On Level

The core Quick Check from the book.

  1. 1.Is x = 4 a solution of x > 1? Yes or no.

  2. 2.Is x = 0 a solution of x < 5? Yes or no.

  3. 3.Write an inequality for: you may spend at most 20 dollars.

  4. 4.Write an inequality for: a number is greater than 7.

  5. 5.Is x = 6 a solution of x greater than or equal to 6? Yes or no.

Challenge

Stretch your thinking.

  1. 1.Write an inequality for: you must be at least 13 years old to join.

  2. 2.Is x = 8 a solution of x less than or equal to 8? Yes or no.

  3. 3.Write an inequality for: a bag can hold at most 50 pounds.