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Chapter 2: Q. 641 (page 222)

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

3(2x-3)<-5or4x-1>3

Short Answer

Expert verified

The required answer is x<23,x>1and the required graphs are

The solution in interval notation is(-鈭�,23)鈭�(1,鈭�)

Step by step solution

01

Step 1. Given Information

The given inequalities are3(2x-3)<-5or4x-1>3

02

Step 2. Calculation

On Solving both the inequalities, we get,

3(2x-3)<-5鈬�2x-3<-53鈬�2x<43鈬�x<234x-1>3鈬�4x>4鈬�x>1

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 x<23orx>1

04

Step 4. Interval notation

On writing the solution in interval notation, we get,

(-鈭�,23)鈭�(1,鈭�)

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