Which absolute value equation represents the number line.

D

Step-by-step explanation:

we have two extreme points : x = -3 and x = 7

now we only need to find the equation in the 4 answer options that is true for both x values.

A is impossible. the left side creates a guaranteed negative value (the absolute value of something is always positive, and then putting a negative sign in front of it creates always a negative value). and the right side is +5. this is therefore always wrong.

B is impossible for the same reasons. the left side is an absolute value and therefore always positive. yet the right side is -5. this is therefore also always wrong.

C is impossible again for the same reasons. the absolute value of x is always positive, the negative sign in front of it makes it an always negative value. then we subtract 2, which makes the negative value even more negative. and on the right side is +5. this is therefore also always wrong.

D is the one option, where left and right side fit together. and using x = -3 gives us

-|-3 - 2| = -5

|-3 -2| = |-5| = 5

-|-3 - 2| is therefore -5, and that is equal to the right side.

and x = 7 gives us

-|7 - 2| = -|5| = -5, and that is equal to the right side.

so, D is confirmed.

this would be 35. 35 + 5 = 40. you take the known constant and subtract by the answer of the equation and you get y.