SAT Mathematics Practice Test 6

Question : 48 of 58

Marks: +1, -0

Two different points on a number line are both 3 units from the point with coordinate

−4

.The solution to which of the following equations gives the coordinates of both points?

$|x+4|=3$
$|x-4|=3$
$|x+3|=4$
$|x-3|=4$

Validate

Solution:

The coordinates of the points at a distance d units from the point with coordinate a on the number line are the solutions to the equation

|x−a|=d

.Therefore, the coordinates of the points at a distance of 3 units from the point with coordinate

−4

on the number line are the solutions to the equation

|x−(−4)|=3

, which is equivalent to

|x+4|=3

.
Choice B is incorrect. The solutions of |x − 4| = 3 are the coordinates of the points on the number line at a distance of 3 units from the point with coordinate 4. Choice C is incorrect. The solutions of

|x+3|=4

are the coordinates of the points on the number line at a distance of 4 units from the point with coordinate

−3

. Choice D is incorrect. The solutions of

|x−3|=4

are the coordinates of the points on the number line at a distance of 4 units from the point with coordinate 3.

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