Question

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

Answer 1

`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`

Answer 2

`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"`

Answer 3

`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`