Question

How do you solve `|10x - 28| + 2> 24`?

Answer 1

`x>5, x < 3/5`

Explanation:

Let's first isolate the absolute value term:

`abs(10x-28)+2>24`

`abs(10x-28)>22`

With absolute values, we need to evaluate the positive aspect and negative aspect (keep in mind that with, say `abs(x)=3`, `x` can be 3 and also can be `-3`, and so when we evaluate the absolute value, we say `x=pm3`. We do the same process for all absolute value questions).

`pm(10x-28)>22`

Positive aspect

`10x-28>22`

`10x>50`

`x>5`

Negative aspect

`-(10x-28)>22`

`-10x+28>22`

`-10x> -6`

we divide by `-10` and so we change the direction of the inequality:

`x < 6/10=3/5`

Putting it together:

`x>5, x < 3/5`