CASE 1. color(red)(5.2x+7 >= 0)5.2x+7≥0
if
5.2x+7 >= 05.2x+7≥0
i.e. x >= -7/5.2i.e.x≥−75.2 or x >= -35/26x≥−3526
then
|5.2x+7| = 5.2x+7|5.2x+7|=5.2x+7
because the modulus of a positive number is the number itself.
therefore in this case 5.2x+7=3.8 => 5.2x = -3.2
=> x=-3.2/5.2 = color(red)(-8/13)
CASE 2. color(red)(5.2x+7 < 0)
if
5.2x+7 < 0
i.e. x < -7/5.2 or x < -35/26
then
|5.2x+7| = -(5.2x+7) = -5.2x-7
because the modulus of a negative number is negative of the number or in other words modulus of a negative number is obtained by multiplying the number with -1.
e.g. -2<0 => |-2| = -(-2) or -1*(-2) = 2
therefore in this case -5.2x-7=3.8 =>-5.2x = 10.8
=> x=-10.8/5.2 = color(red)(-27/13)
Hence, x = color(red)(-8/13) or color(red)(-27/13).
