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9th grade · Math · Unit 11 of 17

Linear Inequalities

Solve and write inequalities

What your child practices

Solving linear inequalities (flipping the sign when dividing by a negative), checking a solution, and writing inequalities from budgets and limits.

Arizona Academic Standards learning standard: A1.A-REI.B.3; A1.A-CED.A.1 · creating and solving linear inequalities in context

How we explain it

Children can open this short lesson before they practice.

  1. Solve an inequality like an equation.
  2. If you multiply or divide by a negative number, flip the sign.
  3. Check with a number from your answer.

Example: Solve −2x + 3 > 11. Subtract 3: −2x > 8. Divide by −2 and flip: x < −4. Answer: x < −4

Linear Inequalities in Arizona

In the Arizona Academic Standards, this is unit 11 of 17 in 9th grade Math, after Function Notation and before Solving Systems.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Arizona Department of Education

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Is x = 3 a solution of 2x < −2?

    • Yes
    • No

  2. Question 2

    Tickets cost $11 each plus a $2 fee. You can spend at most $120. What is the greatest number of tickets you can buy?

    • 12
    • 11
    • 10
    • 9

  3. Question 3

    Solve 4x + 9 ≤ 17.

    • x ≤ −2
    • x ≤ 3
    • x ≥ 2
    • x ≤ 2

  4. Question 4

    You have $70. Shirts cost $9 each and shipping is $8. Which inequality shows how many shirts, s, you can buy?

    • 9s + 8 ≥ 70
    • 9s ≤ 70 + 8
    • 9 + 8s ≤ 70
    • 9s + 8 ≤ 70

  5. Question 5

    You have $30. Shirts cost $14 each and shipping is $3. Which inequality shows how many shirts, s, you can buy?

    • 14 + 3s ≤ 30
    • 14s + 3 ≥ 30
    • 14s + 3 ≤ 30
    • 14s ≤ 30 + 3

  6. Question 6

    Tickets cost $9 each plus a $7 fee. You can spend at most $120. What is the greatest number of tickets you can buy?

    • 15
    • 12
    • 13
    • 14

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