Question

Which of the following statement is true if $\mathrm{x}=-2$ and $\mathrm{y}=8$ $?$

Select all that apply.

• A. $\left|\mathrm{x}\right|\le \left|\mathrm{y}\right|$
• B. $\left|\mathrm{y}\right|\ge \left|\mathrm{x}\right|$
• C. $\left|\mathrm{x}\right|>\left|\mathrm{y}\right|$
• D. $\left|\mathrm{y}\right|<\left|\mathrm{x}\right|$

Answer 1

Answer: (A), (B)

$\left|\mathrm{y}\right|\ge \left|\mathrm{x}\right|$

Explanation for correct option:

Option $\mathbf{\left(}\mathbf{A}\mathbf{\right)}$, Option $\mathbf{\left(}\mathbf{B}\mathbf{\right)}$:

Compare $\left|x\right|$ and $\left|y\right|$.

The absolute value denotes only the numeric value and does not include the sign of the numeric value.

The absolute value of $\mathrm{x}$ and $\mathrm{y}$ are as follows:

$\begin{array}{rcl}\left|x\right|& =& \left|-2\right|\\ & =& 2\\ \left|y\right|& =& \left|8\right|\\ & =& 8\end{array}$

Since $\mathbf{2}\mathbf{\le }\mathbf{8}$, option $\mathbf{\left(}\mathbf{A}\mathbf{\right)}$ is correct.

Since $\mathbf{8}\mathbf{\ge }\mathbf{2}$, option $\mathbf{\left(}\mathbf{B}\mathbf{\right)}$ is correct.

Hence, the correct options are $\mathbf{\left(}\mathbf{A}\mathbf{\right)}$ and $\mathbf{\left(}\mathbf{B}\mathbf{\right)}$.