Two different points on a number line are both 4 units from the coordinate \(-11\). The solution to which of the following equations gives the coordinates of both points?

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If a number is 4 units away from another number, the difference between these two numbers must be 4. Therefore,

$$ x-(-11)=4 $$ $$ x+11=4 $$ $$ x=7 $$

To- obtain the other solution, we need to understand that a distance of negative \(4\) is equivalent to a distance of positive \(4\) . Accordingly,

$$ x-(-11)=-4 $$ $$ x+11=-4 $$ $$ x=-15 $$

A way to combine these two statements is to say that the absolute difference between two numbers is \(4\).

$$ |x-(-11)|=4 $$ $$ |x+11|=4 $$ $$ x=-7 \text{ or } -15 $$

We can find the solutions by inspection. If we drew a number line, \(-7\) and \(-15\) would be the points 4 units to the left and to the right of \(-11\). Only one asnwer choice satisfies both of these values:

$$ \boxed{|x+11|=4} $$