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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.

Washington State Learning Standards learning standard: M.HS.R.AREI.3; M.HS.R.ACED.1 · solving linear inequalities in one variable and creating inequalities from situations

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

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

    Solve 4x + 10 ≤ 14.

    • x ≤ 1
    • x ≤ −1
    • x ≥ 1
    • x ≤ 2

  2. Question 2

    You have $80. Shirts cost $9 each and shipping is $8. Which inequality shows how many shirts, s, you can buy?

    • 9s + 8 ≥ 80
    • 9s ≤ 80 + 8
    • 9s + 8 ≤ 80
    • 9 + 8s ≤ 80

  3. Question 3

    Is x = 7 a solution of 4x − 2 < 4?

    • No
    • Yes

  4. Question 4

    Tickets cost $9 each plus a $2 fee. You can spend at most $100. What is the greatest number of tickets you can buy?

    • 8
    • 9
    • 11
    • 10

  5. Question 5

    Solve −5x − 2 > 28.

    • x > 6
    • x > −5
    • x < −6
    • x > −6

  6. Question 6

    Tickets cost $3 each plus a $6 fee. You can spend at most $50. What is the greatest number of tickets you can buy?

    • 17
    • 14
    • 15
    • 16

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