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Pearson Algebra 1 Common Core, 2011 View details

5. Working With Sets

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Exercise 45 Page 198

To solve the inequality, isolate x.

∅

Practice makes perfect

To solve the inequality, we have to isolate x. By distributing - 3 on the left-hand side and using inverse operations, we can isolate the variable.

- 3(4x+8)+1<- 23-12x

Distr

Distribute - 3

- 12x-24+1<- 23-12x

AddTerms

Add terms

- 12x-23<- 23-12x

AddIneq

LHS+23

- 12x<-12x

AddIneq

LHS+12x

0≮ 0

Since a number can never be less than itself, we reached a contradiction. There are no solutions to this inequality. Therefore, the solution set of this inequality is the empty set, ∅.