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Chapter 2: Q. 433 (page 197)

Explain the steps for solving the compound inequality:

2-7x鈮�5or

4x-3+7>鈥�3

Short Answer

Expert verified

To solve the compound inequality first solve both inequalities separately and then the solution to the compound inequality will contain the solution of the both inequality.

Step by step solution

01

Step 1. Given information. 

We have:

2-7x鈮�5or

4x-3+7>鈥�3

02

Step 2. Solve the inequalities separately. 

First, solve 2-7x鈮�5:

Subtract 2from both sides:

role="math" localid="1644909590831" 2-7x-2鈮�鈥�5-2

-7x鈮�鈥�3

Multiply both sides by -1(reverse the inequality):

-7x-1鈮�鈥�3-17x鈮�鈥�-37x7鈮�-37x鈮�鈥�-37

03

Step 3. Solve the second inequality. 

We have:

4x-3+7>鈥�3

Subtract 7from both sides:

4x-3+7-7>3-74x-3>-44x-34>-44x-3>-1x-3+3>-1+3x>2

04

Step 4. Merge the overlapping intervals. 

The solution to the compound inequality will include both solutions.

Thus, the solution to the compound inequality is:

x鈮�1鈭�x>2

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