Question 719078
I believe that the expected answer is {{{abs(x-5)>2}}}.
 
Mid-way between 3 and 7 on the number line is their average, {{{5=(3+7)/2}}}.
{{{number_line( 600, -2, 12, (5-2), 5, (5+2) )}}}
Numbers that are more than {{{2}}} units away from {{{5}}} are
either to the left of {{{3}}} as is {{{x<3}}}
or to the right of {{{7}}} as in {{{x>7}}} .
 
Absolute value of a difference of two numbers is the distance between those two numbers on the number line.
Inequalities that use absolute value of {{{(x-number)}}}
can have solutions that includes numbers at less than a certain distance from the number or at more than a certain distance from the number.
 
{{{abs(x-10)<4}}} <--> {{{6<x<14}}} means numbers less than {{{4}}} units away from {{{10}}}
{{{abs(x-10)>4}}} <--> {{{system(x<6,x>14)}}} means numbers more than {{{4}}} units away from {{{10}}}