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Chapter 2: Q.2.123 (page 189)

Solve the compound inequality. Graph the solution and write the solution in interval notation.

2(3x+1)鈮�20and4(x-1)<2

Short Answer

Expert verified

Solution:x<32IntervalNotation:(-鈭�,32)

The solution graph is

Step by step solution

01

Step 1. Given information

2(3x+1)鈮�20and4(x-1)<2

02

Step 2. Solve each inequalities

2(3x+1)鈮�202(3x+1)2鈮�2023x+1鈮�103x+1-1鈮�10-13x鈮�93x3鈮�93x鈮�34(x+3)<84(x+3)4<84x+3<2x+3-3<2-3x<-1

03

Step 3.Graph Each solution and Merge Them

Graph of2(3x+1)鈮�20

Graph of4(x-1)<2

Merging both the graphs

04

Step 4.Solution and Interval Notation

Solution:x<32IntervalNotation:(-鈭�,32)

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