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Chapter 2: Q.389. (page 195)

Solve compound Inequalities with "and"

-3(x+4)<0and-1(3x-1)鈮�7

Short Answer

Expert verified

The number that make both Inequalities true is x 鈮� - 2

Interval Notation: [-2, 鈭� )

Step by step solution

01

Step 1.Given information

-3(x+4)<0and-1(3x-1)鈮�7

02

Step 2.Solve Each Inequalities and Draw Graph 

-3(x+4)<0鈬�-3(x+4)-3>0-3(WhenweMultiplyordividebynegativenumber,inequalitieschanges)鈬�x+4>0鈬�x+4-4>0-4鈬�x>-4

-1(3x-1)鈮�7鈬�-1(3x-1)-1鈮�7-1鈬�3x-1鈮�-7鈬�3x-1+1鈮�-7+1鈬�3x鈮�-6鈬�3x3鈮�-63鈬�x鈮�-2

03

Step 3.Graph of each solution

Graph of -3(x+4)<0

Graph of-1(3x-1)鈮�7

Merging both graph

04

Step 4. Interval Notation

The number that make both Inequalities true is x 鈮� - 2

Interval Notation: [-2, 鈭� )

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