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Verify the truth values of the given inequalities and insert the correct inequality symbol in the box.

Mathematics

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Here's a verification of your answers:

1. Which of the following inequalities is true or false?

  • a) −250<−150-250 < -150

    • −250-250 is indeed less than −150-150.
    • Your answer: False.
    • ✅ Correct answer: True. Your answer is ❌ Incorrect.

  • b) 2≤−22 \le -2

    • 2 is not less than or equal to −2-2.
    • Your answer: False.
    • ✅ Correct answer: False. Your answer is ✅ Correct.

  • c) 5>−25 > -2

    • 5 is indeed greater than −2-2.
    • Your answer: True.
    • ✅ Correct answer: True. Your answer is ✅ Correct.

  • d) 6≠66 \ne 6

    • 6 is equal to 6, so 6≠66 \ne 6 is false.
    • Your answer: False.
    • ✅ Correct answer: False. Your answer is ✅ Correct.

  • e) −3=3-3 = 3

    • −3-3 is not equal to 3.
    • Your answer: False.
    • ✅ Correct answer: False. Your answer is ✅ Correct.

  • f) 5≥−25 \ge -2

    • 5 is indeed greater than or equal to −2-2.
    • Your answer: False.
    • ✅ Correct answer: True. Your answer is ❌ Incorrect.

2. In each of the following, insert a correct inequality symbol in the box to make the statement true.

  • a) −5×(−3)?8×(−3)-5 \times (-3) \quad \boxed{?} \quad 8 \times (-3)

  1. Calculate both sides.

        $$
    -5 \times (-3) = 15
    $$
    $$
    8 \times (-3) = -24
    $$

  2. Compare the results.

        $$
    15 > -24
    $$
*   Your symbol: $>$
*   ✅ Correct symbol: $\boxed{>}$. Your answer is ✅ Correct.
    • b) 13×(−2)?7×(−2)13 \times (-2) \quad \boxed{?} \quad 7 \times (-2)

  3. Calculate both sides.

        $$
    13 \times (-2) = -26
    $$
    $$
    7 \times (-2) = -14
    $$

  4. Compare the results.

        $$
    -26 < -14
    $$
*   Your symbol: $>$
*   ✅ Correct symbol: $\boxed{<}$. Your answer is ❌ Incorrect.
    • c) 8×(5)?2×(−5)8 \times (5) \quad \boxed{?} \quad 2 \times (-5)

  5. Calculate both sides.

        $$
    8 \times (5) = 40
    $$
    $$
    2 \times (-5) = -10
    $$

  6. Compare the results.

        $$
    40 > -10
    $$
*   Your symbol: $>$
*   ✅ Correct symbol: $\boxed{>}$. Your answer is ✅ Correct.
    • d) 6×(−4)?3×(−4)6 \times (-4) \quad \boxed{?} \quad 3 \times (-4)

  7. Calculate both sides.

        $$
    6 \times (-4) = -24
    $$
    $$
    3 \times (-4) = -12
    $$

  8. Compare the results.

        $$
    -24 < -12
    $$
*   Your symbol: $>$
*   ✅ Correct symbol: $\boxed{<}$. Your answer is ❌ Incorrect.
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