Question

Which of the following inequalities is not true?|-9| < |9| -2²<30-7≤-51-11 ≥ 0

Answer 1

Recall that:

`|a|=\begin{cases}a{\text{ if }a\geq0} \\ -a\text{ if }a<0\end{cases}.`

Therefore:

`|-9|=9=|9|.`

Therefore the inequality:

`|-9|<|9|`

is not true.

Now, notice that:

`\begin{gathered} -2^2=-4<0<3, \\ 0-7=-7\leq-5, \end{gathered}`

Therefore the second and third inequalities are true.

Finally, notice that:

`1-11=-10<0.`

Therefore the last inequality is not true.

Answer: First and last inequalities.