Question

How do you solve `|2x - 4| + 2> 8`?

Answer 1

`x>5 or x<-1`

Explanation:

In order to solve:

`|2x−4|+2>8` ,

Find a way to get `x` on a side by itself. (Isolate the absolute value)

First, subtract `2` from both sides to cancel it from the left side.

`|2x−4|+cancel(2) -cancel(2)> 8 -2`

Giving you:

`|2x−4| > 6`

Now, set up an OR statement.
This looks like this:

(absolute value quantity) > (number on other side)
OR
(absolute value quantity) < -(number on other side)

Which would look like this when substituted:

`|2x−4| > 6`
OR
`|2x−4| < - 6`

---

Now, we solve for each by taking away the absolute value signs.

1. `2x−4 > 6`
   [add 4 to both sides]
   `2xcancel(-4)cancel(+4) >6 +4`
   [divide by 2 on both sides]
   `(cancel(2)x)/cancel(2) > 10/2`
   [simplify]
   Solution : `x>5`
   .
   .

2. `2x−4< - 6`
   [add 4 to both sides]
   `2xcancel(-4)cancel(+4) < -6 +4`
   [divide by 2 on both sides]
   `(cancel(2)x)/cancel(2) < (-2)/2`
   [simplify]
   Solution : `x<-1`

Now, we combine both solutions to get the final answer.

`x>5 or x<-1`