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9th grade · Math · Unit 6 of 16

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.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: A.5(B) · solving linear inequalities in one variable

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 Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 6 of 16 in 9th grade Math, after Multi-Step Equations 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: Texas Education Agency (TEA)

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

    Tickets cost $6 each plus a $6 fee. You can spend at most $100. What is the greatest number of tickets you can buy?

    • 15
    • 12
    • 14
    • 16

  2. Question 2

    You have $90. Shirts cost $4 each and shipping is $4. Which inequality shows how many shirts, s, you can buy?

    • 4s + 4 ≥ 90
    • 4s + 4 ≤ 90
    • 4 + 4s ≤ 90
    • 4s ≤ 90 + 4

  3. Question 3

    Is x = 1 a solution of 2x + 3 < −2?

    • No
    • Yes

  4. Question 4

    Solve −4x + 8 < −20.

    • x < 8
    • x > 7
    • x < −7
    • x < 7

  5. Question 5

    Solve −4x − 7 ≤ −15.

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

  6. Question 6

    Tickets cost $7 each plus a $7 fee. You can spend at most $50. What is the greatest number of tickets you can buy?

    • 6
    • 7
    • 8
    • 4

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