How do you solve this equation with absolute values? #-10|14-r|color(blue)(-2)=-7#

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Answer 1 · 2018-02-12T17:36:16

#r = 13 1/2 or r = 14 1/2#

You need to isolate the absolute value part first - the same as for a normal equation.

#-10|14-r|color(blue)(-2)=-7" "larr# move the #-2#

#-10|14-r| = -7color(blue)(+2)#

#-10|14-r|= color(blue)(-5)" "larr div -10#

#|14-r| = (-5)/(-10) = 1/2#

THere are now two cases to consider.

The answer can be #+1/2 or -1/2#

#14-r = +1/2color(white)(wwwwwwww)14-r=-1/2#

#14-1/2 = rcolor(white)(wwwwwwwwww)14+1/2=r#

#13 1/2 = rcolor(white)(wwwwwwwwwwww)14 1/2 =r#