Question

How do you solve |5x-6|=3?

Answer 1

`x = 9/5` and `x = 3/5`

Explanation:

Because this problem contains the absolute value function we need to give it special attention.

The absolute value function transforms a negative or a positive number into a positive number.

Therefore, we need to solve the term inside the absolute value for both the positive and negative value it is equated to, in this case +3 and -3.

Solution 1)

`5x - 6 = 3`

`5x - 6 + color(red)(6) = 3 + color(red)(6)`

`5x - 0 = 9`

`5x = 9`

`(5x)/color(blue)(5) = 9/color(blue)(5)`

`(color(blue)(cancel(color(black)(5)))x)/cancel(color(blue)(5)) = 9/color(blue)(5)`

`x = 9/5`

Solution 2)

`5x - 6 = color(red)(-3)`

`5x - 6 + color(red)(6) = -3 + color(red)(6)`

`5x - 0 = 3`

`5x = 3`

`(5x)/color(blue)(5) = 3/color(blue)(5)`

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

`x = 3/5`

Answer 2

`x=3/5" and "x=9/5` are solutions

Explanation:

Given:`" "|5x-6|=3`

So in effect we have:

`|+-3|=+3`

So everything inside the | | must end up as positive or negative 3.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Set "5x-6=-3)`

Add 6 to both sides

`5x=+3`

Divide both sides by 5

`color(blue)(x=+3/5)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Set "5x-6=+3)`

Add 6 to both sides

`5x=+9`

Divide both sides by 5

`color(blue)(x=+9/5)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(green)("Putting it all together")`

`|5x-6|=+3`

`x=3/5" and "x=9/5` are solutions