Testinar Grade 6 math

Writing Inequalities

Students will build Grade 6 mastery of writing inequalities using models, equations, and test-style reasoning.

CH03-08 Expressions and Equations
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. A roller coaster requires riders to be at least \(48\) inches tall. Which inequality describes the height \(h\) (in inches) needed to ride?

    1. \(h<48\)
    2. \(h>48\)
    3. \(h\leq48\)
    4. \(h\geq48\)

  2. The speed limit on the highway is no more than \(65\) miles per hour. Which inequality represents the allowed speed \(s\)?

    1. \(s>65\)
    2. \(s\leq65\)
    3. \(s\geq65\)
    4. \(s=65\)

  3. A swimming pool must have a temperature greater than \(78\) degrees Fahrenheit. Which inequality matches this requirement for temperature \(t\)?

    1. \(t\leq78\)
    2. \(t=78\)
    3. \(t>78\)
    4. \(t<78\)

  4. To qualify for a school club, you must have no less than a \(3.0\) grade point average. Which inequality describes the minimum GPA \(g\)?

    1. \(g<3.0\)
    2. \(g>3.0\)
    3. \(g\leq3.0\)
    4. \(g\geq3.0\)

  5. A discount applies when you spend less than \($50\). If \(d\) represents the amount you spend, which inequality is correct?

    1. \(d<50\)
    2. \(d\leq50\)
    3. \(d>50\)
    4. \(d\geq50\)

  6. Which phrase best describes the inequality \(x\geq12\)?

    1. Less than \(12\)
    2. Greater than \(12\)
    3. No more than \(12\)
    4. At least \(12\)

  7. The weight of a piece of luggage must not exceed \(50\) pounds. Which inequality best represents this, where \(w\) is the weight?

    1. \(w>50\)
    2. \(w\leq50\)
    3. \(w<50\)
    4. \(w\geq50\)

  8. You need to save more than \($200\) for a new computer. If \(s\) is the amount you save, which inequality represents this?

    1. \(s<200\)
    2. \(s=200\)
    3. \(s\leq200\)
    4. \(s>200\)
Teacher and parent reference

Answer key and explanations

  1. D. \(h\geq48\)

    "At least \(48\)" means \(48\) or more, which is written as \(h\geq48\).

  2. B. \(s\leq65\)

    "No more than" means at most \(65\), which allows \(65\) and anything less: \(s\leq65\).

  3. C. \(t>78\)

    "Greater than" means strictly more, not equal: \(t>78\). This excludes \(78\) itself.

  4. D. \(g\geq3.0\)

    "No less than \(3.0\)" means \(3.0\) or more: \(g\geq3.0\).

  5. A. \(d<50\)

    "Less than \($50\)" means strictly below \(50\): \(d<50\).

  6. D. At least \(12\)

    \(x\geq12\) means \(x\) can equal \(12\) or be larger, which matches "at least \(12\)."

  7. B. \(w\leq50\)

    "Must not exceed" means at most \(50\): \(w\leq50\).

  8. D. \(s>200\)

    "More than \(200\)" means strictly greater: \(s>200\).

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