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Pearson Algebra 1 Common Core, 2011 View details

5. Working With Sets

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Exercise 41 Page 198

To solve the inequality, isolate x.

∅

Practice makes perfect

To solve the inequality, we have to isolate x. By distributing - 2 on the left-hand side and using inverse operations, we can isolate the variable.

- 2(3x+7)>- 14-6x

Distr

Distribute - 2

- 6x-14>- 14-6x

AddIneq

LHS+14>RHS+14

-6x>- 6x

AddIneq

LHS+6x>RHS+6x

0≯ 0

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