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

3 Answers
Mar 29, 2018

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

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

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