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Chapter 2: Q. 9 (page 126)

Solve the inequality. Graph the solution set.

4x+1鈮�7

Short Answer

Expert verified

The solution set of the given inequality is:

(-鈭�,-2]鈭�[32,鈭�)

The graph of the solution set is given as:

Step by step solution

01

Step 1. Given information 

The given inequality is4x+1鈮�7

02

Step 2.  Open the modulus function 

We know that, from the principle of absolute value, for x鈮�a, we have:

-a鈮�x鈮�a.

Similarly, for 4x+1鈮�7, we have:

-7鈮�4x+1鈮�7

03

Step 3. Solving the inequality 

Solving the inequality using properties, we get :

-7鈮�4x+1鈮�7-7-1鈮�4x鈮�7-1-8鈮�4x鈮�6-2鈮�x鈮�32

04

Step 4. Verify the solution set 

Substituting x=2in the given inequality, we get:

4x+1鈮�74脳-2+1鈮�7-8+1鈮�7-7鈮�77鈮�7

This is true.

Hence, the solution set of the given inequality is-2鈮�x鈮�32orx鈮�-2orx鈮�32

05

Step 5. Graph the solution set 

The graph of the solution set is given as:

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