Question

Which values of x will make the absolute value equation true? |x – 3| = 40
A. {–43, –37}
B. {43, –37}
C. {40, –40}
D. {43, 37}

Answer 1

Absolute value stripes make everything inside those stripes positive (or equal to 0).

Therefore
$|x - 3| = 40$
gives us two equations. The first one is the normal equation and on the second equation 40 will be replaced by -40 (because everything BETWEEN the stripes can also be negative, but those stripes make them positive afterwards). Thus:

$(x - 3) = 40 \: \: \: \: or \: \: \: (x - 3) = - 40$
Add 3 to both sides (in both equations)

$x = 43 \: \: \: or \: \: \: x = - 37$
Hence, B. is the correct answer.