Chapter SH, Problem 2.1.12EP

To determine

The correct inequality for the given expression

Answer to Problem 2.1.12EP

  $\left|-7\right|>\left|-4\right|$

Explanation of Solution

Given information:

  $\left|-7\right|\circ \left|-4\right|$

Concept Used:

When two quantities are not equal, the comparison between them is often presented by certain symbols, this comparison is known as inequality and the symbols used for such comparison are known as inequality symbols.

There are four inequality symbols, $>$ , $<$ , $\ge$ , $\le$ namely “greater than”, “less than”, “greater than or equal to” and “less than or equal to” respectively.

We know that on a number line, integers are placed at an interval of one and value if integers increases as we move left to right on the number line. Also, distance of a number from zero on number line is known as its absolute value.

Absolute value of any number is always positive, i.e.-

  $\begin{array}{l}\left|a\right|=a\\ \left|-a\right|=a\end{array}$

Calculation:

In the given expression-

  $\left|-7\right|\circ \left|-4\right|$

We can say-

  $\begin{array}{l}\left|-4\right|=4\text{and}\\ \left|-7\right|=7\end{array}$

We can clearly say that $\left|-4\right|$ is smaller than $\left|-7\right|$ and it would lie to the left on the number line, hence the inequality will be given by-

  $\left|-7\right|>\left|-4\right|$