How do you solve #abs(4x+1)=11#?

3 Answers
Mar 29, 2018

Answer:

#x=5/2 \, x=-3#

Explanation:

#|4x+1|=11#
#4x+1=11 \, 4x+1=-11# (Definition of #|a|#)
#4x=11-1 \, 4x=-11-1#
#4x=10 \, 4x=-12#
#x=10/4 \, x=-12/4#
#x=5/2 \, x=-3#

Mar 29, 2018

Answer:

#x=-3" or "x=5/2#

Explanation:

#"the expression inside the bars of the absolute value can"#
#"be positive or negative"#

#color(blue)"Positive value"#

#4x+1=11#

#rArr4x=11-1=10#

#rArrx=10/4=5/2#

#color(blue)"Negative value"#

#-(4x+1)=11#

#rArr-4x-1==11#

#rArr-4x=11+1=12#

#rArrx=12/(-4)=-3#

#color(magenta)"As a check"#

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

#|(4xx5/2)+1|=|11|=11=" right side"#

#|(4xx-3)+1|=|-11|=11=" right side"#

#rArrx=-3" or "x=5/2" are the solutions"#

Mar 29, 2018

Answer:

#x=2.5#

Explanation:

The lines are just saying absolute value which is the distance from zero. So all you have to do is get rid of those...
#4x+1=11#
subtract 1 from both sides and get... #4x=10#
then, divide 4 on both sides and you get #x=2.5#