Question

Which number line represents the solutions to |x + 4| = 2?

Answer 1

Answer : The first line represents the solutions to |x + 4| = 2.

Given absolute value equation : |x + 4| = 2

To solve an absolute value equation , first step is to remove the absolute value sign.

An absolute value always give a positive result whereas the expression inside the absolute sign can be  positive or negative.

Hence, to remove an absolute value we will take both positive an negative value such that

-(x+4)=2 or (x+4)=2

⇒ x+4=-2 or x+4=2

⇒x=-2-4 or x=2-4 [subtract 4 from both the sides]

⇒x= -6 or x= -2 which is given by the first line.

Therefore first line represents the solutions to |x + 4| = 2.

Answer 2

The answer is the first one because the left of the equal sign in absolute value, which sets an integer to a positive integer.