How do you solve the inequality #9 > -3 (x - 1) ≥ -12#?

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Answer 1 · 2018-06-24T08:40:39

# -2 < x <= 5#

Given: #9 > -3(x-1)>= -12#

#color(blue)("Manipulate the same way you do equation.")#
#color(blue)("but be mindful about the inequality sign")#

Divide throughout by 3 (does not change the signs)

#3 > -x+1 >= -4#

Subtract 1 throughout

#2 > -x >= -5#

#color(brown)("Consider the part: "-x >= -5)#

Swap sides and change the negatives to positives. Keep the inequality the same way round.

Same thing as: add 5 to both sides and add #x# to both sides and keep the inequality the same way round.

Same thing as: multiply both sides by (-1) and turn the inequality sign the other way round.

#5 >= x color(white)("ddd")larr# This is the same thing as #x <= 5#

#color(brown)("Consider the part: "2 > -x)#

Swap sides and change the signs but keep the inequality the same way round.

#x > -2#

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#color(brown)("Putting it all together")#

# -2 < x <= 5#