Introduction and properties of inequations

Problems

Check if the following inequalities are true or false:

  1. $$103 > 25 $$

  2. $$-62 > 4.5 $$

  3. $$42 \leqslant \dfrac{84}{2} $$

  4. $$-4 > -5 $$

  5. $$1 > 1 $$

  6. $$0 < 3 < -3.1 $$
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Development:

  1. $$103$$ is greater than $$25$$.
  2. $$-62$$ is a negative number, so it is less than $$4.5$$ (nombre positiu).
  3. $$84$$ divided by $$2$$ is $$42$$, hence the expression is correct: $$42$$ is equal to $$42$$.
  4. $$-4$$ is greater than $$-5$$ (since the numbers are negative).
  5. $$1$$ is equal to $$1$$, but $$1$$ is not greater than $$1$$, in any case, it would be correct if we said that $$1$$ is greater than or equal to $$1$$.
  6. In this case, we have a double inequality. We have to check that both inequalities are true: $$0$$ is less than $$3$$, but $$3$$ is not less than $$-3.1$$ since this is a negative number. Consequently, the expression is false.

Solution:

  1. True.

  2. False.

  3. True.

  4. True.

  5. False.

  6. False.
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