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