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Chapter 2: Q.380. (page 195)

In the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.

5x-2<8and6x+9鈮�3

Short Answer

Expert verified

Thenumberthatmakebothinequalitiestrueis-1鈮�x<2IntervalNotation:[-1,2)

Step by step solution

01

Step 1. Given information

5x-2<8and6x+9鈮�3

02

Step 2. Solve Each Inequalities

5x-2<8鈬�5x-2+2<8+2鈬�5x<10鈬�5x5<105鈬�x<26x+9鈮�3鈬�6x+9-9鈮�3-9鈬�6x鈮�-6鈬�6x6鈮�-66鈬�x鈮�-1

03

Step 3. Graph each solution

Graph of x<2

Graph of x鈮�-1

04

Step 4.Merge the graph of each solution

05

Step 5.Interval Notation

Thenumberthatmakebothinequalitiestrueis-1鈮�x<2IntervalNotation:[-1,2)

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