Question

How do you solve `abs(3x-1)=14`?

Answer 1

The solutions are `S={-13/3, 5}`

Explanation:

`3x-1=14`

`3x=14+1=15`

`x=5`

`-3x+1=14`

`3x=-14+1=-13`

`x=-13/3`

Answer 2

See the entire solution process below:

Explanation:

The absolute value function takes any negative or positive term and transforms it into its positive form. Therefore, you need to solve the term within the absolute value for both the negative and positive of what it is equated to giving two answers.

Solution 1)

`3x - 1 = -14`

`3x - 1 + color(red)(1) = -14 + color(red)(1)`

`3x - 0 = -13`

`3x = -13`

`(3x)/color(red)(3) = -13/color(red)(3)`

`(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = -13/3`

`x = -13/3`

Solution 2)

`3x - 1 = 14`

`3x - 1 + color(red)(1) = 14 + color(red)(1)`

`3x - 0 = 15`

`3x = 15`

`(3x)/color(red)(3) = 15/color(red)(3)`

`(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 5`

`x = 5`

The solution to this problem is:

`x = -13/3` and `x = 5`

Answer 3

`x=-13/3" or "x=5`

Explanation:

There are 2 solutions to equations involving the `color(blue)"absolute value"`

`rArr3x-1=color(red)(+-)14`

`color(blue)"Solution 1"`

`3x-1=14`

add 1 to both sides.

`3xcancel(-1)cancel(+1)=14+1`

`rArr3x=15rArrx=5`

`color(blue)"Solution 2"`

`3x-1=-14`

add 1 to both sides.

`3xcancel(-1)cancel(+1)=-14+1`

`rArr3x=-13rArrx=-13/3`

`color(blue)"As a check"`

`"left side "=|(3xx5)-1|=|15-1|=|14|=14color(white)(xx)✔︎`

`"left side "=|(cancel(3^1)xx-13/cancel(3)^1)-1|=|-14|=14color(white)(xx)✔︎`

`rArrx=5" or " x=-13/3" are the solutions"`