Question

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

Answer 1

the first number line

given | x + 4 | = 2

removing the bars from the absolute value gives

x + 4 = 2 or x + 4 = - 2

x = 2 - 4 or x = - 2 - 4

x = - 2 and x = - 6 ← solutions

these are indicated on the number line by a solid circle at - 2, - 6

Answer 2

The solution is represented by the first number line, wich has the solutions x=-6 and x=-2.

Explanation:

We have an absolute value function for the equation. This means that we should have two differents solution in the real number line. As the equation is

`|x+4|=2`

when we clear out the absolute value, we will have two possible solutions:

`x+4=2`

and

`-(x+4)=2`

now we clear x from both equations

`x+4=2 \Leftrightarrow x=2-4 \Leftrightarrow x=-2`

`-(x+4)=2 \Leftrightarrow -x-4=2 \Leftrightarrow -2-4=x \Leftrightarrow x=-6`

Then, we have that x=-2 and x=-4 are the solutions for the equation, and therefore the number line that represents the solution is the first one, where the points -6 and -2 are highlighted.