Question

In the following exercises, fill in$<,>,$or$=$for each of the following pairs of numbers.

$$\begin{gathered} \left(\text{a}\right)-\left|7\right|............-\left|-7\right| \\ \left(\text{b}\right)-8............-\left|-8\right| \\ \left(\text{c}\right)\left|-13\right|...........-13 \\ \left(\text{d}\right)\left|-12\right|...........-\left(-12\right) \end{gathered}$$

Short answer

The Complete statements are

$$\begin{gathered} \left(\text{a}\right)-\left|7\right|\mathbf{=}-\left|-7\right|\left(\text{equalsign}\right) \\ \left(\text{b}\right)-8\mathbf{=}-\left|-8\right|\left(\text{equalsign}\right) \\ \left(\text{c}\right)\left|-13\right|\mathbf{>}-13\left(\text{greaterthansign}\right) \\ \left(\text{d}\right)\left|-12\right|\mathbf{=}-\left(-12\right)\left(\text{equalsign}\right) \end{gathered}$$

Step-by-step solution

Step 1. Given information

The given statements are

$$\begin{gathered} \left(\text{a}\right)-\left|7\right|..........-\left|-7\right| \\ \left(\text{b}\right)-8...............-\left|-8\right| \\ \left(\text{c}\right)\left|-13\right|..............-13 \\ \left(\text{d}\right)\left|-12\right|..............-\left(-12\right) \end{gathered}$$

Part a.Step 1. Fill the blank

$$\begin{gathered} \left(\text{a}\right)-\left|7\right|........-\left|-7\right|=-7........-7 \\ \Rightarrow -7\mathbf{=}-7 \end{gathered}$$

Hence,$-\left|7\right|\mathbf{=}-\left|-7\right|$

Part b.Step 1.Fill the blank

$$\begin{gathered} \left(\text{b}\right)-8\mathbf{=}-\left|-8\right|=-8........-8 \\ \Rightarrow -8\mathbf{=}-8 \end{gathered}$$

Hence,$-8\mathbf{=}-\left|-8\right|$

Part c.Step 1.Fill the blank

$$\begin{gathered} \left(\text{c}\right)\left|-13\right|.........-13=13.......-13 \\ \Rightarrow 13\mathbf{>}-13 \end{gathered}$$

Hence,$\left|-13\right|\mathbf{>}-13.$

Part d.Step 1.Fill the blank

$$\begin{gathered} \left(\text{d}\right)\left|-12\right|.......-\left(-12\right)=12..........12 \\ \Rightarrow 12\mathbf{=}12 \end{gathered}$$

Hence,$\left|-12\right|\mathbf{=}-\left(-12\right).$