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Chapter 2: Q. 642 (page 222)

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

34x-5鈮�2and-3(x+1)鈮�6

Short Answer

Expert verified

The required answer is x鈮�14,x鈮�0and the required graphs are

The solution in interval notation is(-鈭�,鈭�)

Step by step solution

01

Step 1. Given Information

The given inequalities are12x-3鈮�4or13(x-6)鈮�-2

02

Step 2. Calculation

On Solving both the inequalities, we get,

x2-3鈮�4鈬�x2鈮�7鈬�x鈮�14x-63鈮�-2鈬�x-6鈮�-6鈬�x鈮�0

03

Step 3. Draw

Draw each solution on the number line.

Now, graph the numbers that make both the inequalities true.

Numbers that satisfy either of inequalities are-鈭�<x<鈭�

04

Step 4. Interval notation

On writing the solution in interval notation, we get,

(-鈭�,鈭�)

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