Solving linear inequalities and solution sets · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
En anglais

Solving linear inequalities and solution sets

Mathematics · Algebra · ages 15-16
Name ______________________   Date ____________

  1. Solve 5x - 4 < 16. What is the largest whole number in the solution set?

    Answer: ______________

  2. Adding a number to both sides of an inequality changes the direction of the sign.

    Circle one:   True   False

  3. Solve 2x + 1 ≤ 8. Which description gives its solution on a paper number line?

    • Closed circle at 7/2, shade left.
    • Open circle at 7/2, shade right.
    • Closed circle at 7/2, shade right.
    • Open circle at 7/2, shade left.

  4. Solve 2x + 5 > 11. What is the solution?

    • x is greater than 6
    • x is less than 3
    • x is greater than 3
    • x is greater than 8

  5. How many integers satisfy -11 ≤ 1 - 3x < -2?

    Answer: ______________

  6. The inequality -x <= 4 has the solution x >= -4.

    Circle one:   True   False

  7. Sam writes 10 - 4x ≤ 2, then -4x ≤ -8, then x ≤ 2. Which correction is needed?

    • Add 10 to both sides instead of subtracting 10.
    • Divide both sides by positive 4 instead of negative 4.
    • Change -8 to positive 8 before dividing both sides.
    • Reverse ≤ to ≥ when dividing both sides by -4.

  8. Solve 1 < 2x - 3 <= 5. How many whole numbers are in the solution set?

    Answer: ______________

  9. Which value is in the solution set of x < -2 or x >= 5?

    • -2
    • 3
    • 0
    • 5

  10. Solve -5 < 3x + 2 ≤ 7. How many integers are in the solution set?

    Answer: ______________

LightMySky · lightmysky.comW1-mt_QkG3Cw5VgM-s1

Answer key

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

Solving linear inequalities and solution sets W1-mt_QkG3Cw5VgM-s1

  1. 3 · Add 4 to get 5x < 20, so x < 4, and the largest whole number below 4 is 3.
  2. False · Adding or subtracting the same number from both sides keeps the order the same, so the sign does not change.
  3. Closed circle at 7/2, shade left. · Subtract 1 and divide by positive 2 to get x ≤ 7/2. The boundary is included and smaller values work, so use a closed circle and shade left.
  4. x is greater than 3 · Subtract 5 from both sides to get 2x > 6, then divide by 2 to get x > 3.
  5. 3 · Subtract 1: -12 ≤ -3x < -3. Divide by -3 and reverse both signs: 4 ≥ x > 1, or 1 < x ≤ 4. The integers are 2, 3 and 4.
  6. True · Multiply by -1 and flip the sign: x >= -4.
  7. Reverse ≤ to ≥ when dividing both sides by -4. · The subtraction is correct. Dividing -4x ≤ -8 by -4 gives x ≥ 2 because negative division reverses the sign.
  8. 2 · Add 3 to get 4 < 2x <= 8, divide by 2 to get 2 < x <= 4, and the whole numbers are 3 and 4.
  9. 5 · The set is x < -2 or x >= 5. The >= sign includes 5, while -2, 3 and 0 are outside the set.
  10. 4 · Subtract 2 and divide by 3: -7/3 < x ≤ 5/3. The integers are -2, -1, 0 and 1, so there are 4.
Worksheet · LightMySky