How do you solve the inequality #–9(x – 2) < –72#?

1 Answer
Júlio B. · Tanish J.
Dec 30, 2015

S = #( x in RR | x > 10)#

Explanation:

#-9# multiplies the parenthesis content, so:
#-9 * x + (-9) * -(2)#
#-9x + 18 < -72#.

#18# passes to the other side and changes it sign:

#-9x < -72 - 18#

#-9x < -90#

Now, #-9# that multiplies #x# passes to the other side, dividing #-90#:

#x > (-90)/(-9)#

Notice that the direction of inequality has changed because either side was divided by a negative number.

Double negative equals positive, and #90/9 = 10#, and the sense
of direction changes because as a rule if a negative number is multiplied or divided to both sides of an inequality the sense of direction changes.
#x >10#.

Solution set: S = #( x in RR | x > 10)#.

This can be checked by substituting any number greater than positive 10 into the original inequality, say 11, and we have

#-9(11-2) = -81 < -72#

which is true!

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