Question

What inequality shows that −4 is greater than a number 4 units to its left?

Answer 1

To express that \(-4\) is greater than a number that is \(4\) units to its left, we first need to determine what it means for a number to be \(4\) units to the left of \(-4\).

A number \(x\) that is \(4\) units to the left of \(-4\) can be expressed as:

\[
x = -4 - 4 = -8
\]

Now, we want to show that \(-4\) is greater than \(x\). Thus, we can write the inequality:

\[
-4 > x
\]

Substituting \(x = -8\) gives us:

\[
-4 > -8
\]

Since this inequality holds true, we can conclude that the appropriate inequality showing that \(-4\) is greater than a number \(4\) units to its left is:

\[
-4 > x
\]

where \(x\) is any number \(4\) units to the left of \(-4\). More generally, it can also be expressed as:

\[
-4 > x \quad \text{where} \quad x = -4 - 4
\]