Question

1. Solve -21 < -3x + 6 < 12

Answer 1

Answer:

-2<x<9

Step-by-step explanation:

−21<−3x+6<12-21<-3x+6<12

Move all terms not containing xx from the center section of the inequality.

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−27<−3x<6-27<-3x<6

Divide each term in the inequality by −3-3.

−27−3>−3x−3>6−3-27-3>-3x-3>6-3

Divide −27-27 by −3-3.

9>−3x−3>6−39>-3x-3>6-3

Cancel the common factor of −3-3.

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9>x>6−39>x>6-3

Divide 66 by −3-3.

9>x>−29>x>-2

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

−2<x<9-2<x<9

The result can be shown in multiple forms.

Inequality Form:

−2<x<9-2<x<9

Interval Notation:

(−2,9)