Fill in $<$, $>$or $=$for each of the following pairs of numbers:

(a) localid="1644070592762" $-9\_\_-\left|-9\right|$

(b) localid="1644070601216" $2\_\_-\left|-2\right|$

(c)localid="1644070617682" $-8\_\_\left|-8\right|$

(d)localid="1644070630416" $-\left(-9\right)\_\_\left|-9\right|$

The absolute value of a number $x$is equal to the distance between$x$and 0 on the number line.

The given statement is $-9\_\_-\left|-9\right|$.

On the number line, the distance between 0 and $-9$is 9 units. So, $\left|-9\right|=9$.

Simplify the absolute value bars in the given statement.

$-9\_\_-9$

The number $-9$is equal to $-9$. This implies that,

$-9\underline{=}-9$

So, the blank must be filled by $=$and the statement becomes $-9\underline{=}-\left|-9\right|$.

The given statement is $2\_\_-\left|-2\right|$.

On the number line, the distance between 0 and $-2$is 2 units. So, $\left|-2\right|=2$.

Simplify the absolute value bars in the given statement.

$2\_\_-2$

The number 2 is greater than $-2$. This implies that,

role="math" localid="1644069216159" $2\underline{>}-2$

So, the blank must be filled by $>$and the statement becomes $2\underline{>}-\left|-2\right|$.

The given statement is $-8\_\_\_\left|-8\right|$.

On the number line, the distance between 0 and $-8$is 8 units. So, $\left|-8\right|=8$.

Simplify the absolute value bars in the given statement.

$-8\_\_\_8$

The number $-8$is less than 8. This implies that,

$-8\underline{<}8$

So, the blank must be filled by $<$and the statement becomes $-8\underline{<}\left|-8\right|$.

The given statement is $-\left(-9\right)\_\_\_\left|-9\right|$.

On the number line, the distance between 0 and $-9$is 9 units. So, role="math" localid="1644069850242" $\left|-9\right|=9$.

Simplify the absolute value bars in the given statement.

$$\begin{gathered} -\left(-9\right)\_\_\_9 \\ 9\_\_\_9 \end{gathered}$$

The number 9 is equal to 9. This implies that,

$9\underline{=}9$

So, the blank must be filled by $=$and the statement becomes $-\left(-9\right)\underline{=}\left|-9\right|$.