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

1 Answer

Answer:

#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#