Inequalities and their solution sets · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Inequalities and the number line

Mathematics · Algebra · ages 11-14
Name ______________________   Date ____________

  1. The solution of x > 6 is shown on a number line. Which description matches it?

    • A closed circle on 6 with the arrow shading left
    • A closed circle on 6 with the arrow shading right
    • An open circle on 6 with the arrow shading right
    • An open circle on 6 with the arrow shading left

  2. Is 5 a solution of the inequality x is greater than or equal to 5?

    Circle one:   True   False

  3. Which symbol means 'at least'?

    • <
    • ≥
    • =

  4. In the inequality x ≤ 7, the number 7 is one of the solutions.

    Circle one:   True   False

  5. Is -1 a solution of x + 4 > 2?

    Circle one:   True   False

  6. Solve 2x + 1 < 9 for x.

    • x < 3
    • x < 4
    • x < 5

  7. A parking garage sign says, 'Height limit: less than 7 feet.' Which inequality describes allowed heights, h?

    • h ≥ 7
    • h < 7
    • h ≤ 7

  8. Which value of x makes 3x + 1 < 10 true?

    • 2
    • 3
    • 4
    • 5

  9. Jordan solved 3x + 2 < 20 and got x < 6. He then says 6 itself is one of the solutions. What mistake did he make?

    • Plugging in 6 makes both sides equal, not less than, so 6 is not a solution
    • He should have gotten x > 6 instead
    • He needed to add 2 instead of subtracting it

  10. A charity says donations must be more than $20 to get a receipt. Which amount would NOT get a receipt?

    • $20
    • $25
    • $30
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Inequalities and the number line W1-mt_i2F1nWxJjv-s1

  1. An open circle on 6 with the arrow shading right · > means 6 itself is not included, so the circle is open, and bigger numbers go to the right.
  2. True · 5 is allowed because the symbol means greater than OR equal to, so 5 itself counts.
  3. ≥ · 'At least' means the value or anything bigger is fine, so we use ≥.
  4. True · ≤ means 'less than or equal to,' so 7 itself counts as a solution.
  5. True · Solving gives x > -2, and -1 is greater than -2.
  6. x < 4 · Subtract 1 from both sides: 2x < 8. Divide by 2: x < 4.
  7. h < 7 · 'Less than' does not include 7 itself, so we use the strict symbol <.
  8. 2 · Solving gives x < 3, and 2 is the only choice smaller than 3.
  9. Plugging in 6 makes both sides equal, not less than, so 6 is not a solution · Putting x = 6 into 3x + 2 < 20 gives 20 < 20, which is false, so 6 is not included.
  10. $20 · 'More than $20' is a strict inequality, so 20 itself does not count, only amounts above it.
Worksheet · LightMySky