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:

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