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Which of the following is equivalent to 27 − 2(×+2)<-4-3(1-×)

A 6x<-9
B. -×<-16
C. -2×<-17
D. -5×<-10

User Bozena
by
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1 Answer

4 votes

The answer is 6x > 42/5.

Let's solve the equation one step at a time.

27 − 2(×+2)<-4-3(1-×)

Distribute the -2 in the second term on the left side:

27 − 2(×+2)<-4-3(1-×)

27 - 2x - 4 < -4 - 3 + 3x

27 - 2x - 4 < -7 + 3x

Combine the x terms on the left side:

27 - 2x - 4 < -7 + 3x

-2x + 23 < -7 + 3x

Combine the numeric terms on the right side:

-2x + 23 < -7 + 3x

-2x + 23 < 16 + 3x

Combine the x terms on the right side:

-2x + 23 < 16 + 3x

-5x + 23 < 16

Move the numeric term to the right sid

-5x + 23 < 16

-5x < -7

Isolate x by dividing both sides by its coefficient:

-5x < -7

x > 7/5

Rewrite the inequality to match the answer choices:

x > 7/5

6x > 42/5

The answer is 6x > 42/5.

User Goseib
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