Verified answer

Subtract 2 from both sides

|4x - 3| > 9

There are two possibilities

1. if 4x - 3 < 0

then

-(4x - 3) > 9

3 - 4x < 9

x < -6/4 or -3/2

2. If 4x - 3 > 0

then

4x - 3 > 9

4x > 12

x > 3

Answer

(-infinity, -3/2) and (3, +infinity)

1. Since 2 does not contain the variable to solve for, move it to the right-hand side of the inequality by subtracting 2 from both sides.

|4x-3|>-2+11

2. Add 11 to -2 to get 9.

|4x-3|>9

3. Remove the absolute value term. This creates a \ on the right-hand side of the equation because |x|=\x.

4x-3>\(9)

4. Set up the + portion of the \ solution.

4x-3>9

5. Move all terms not containing x to the right-hand side of the inequality.

4x>12

6. Divide each term in the inequality by 4.

x>3

7. Set up the - portion of the \ solution. When solving the - portion of an inequality, flip the direction of the inequality sign.

4x-3<-(9)

8. Multiply -1 by the 9 inside the parentheses.

4x-3<-9

9. Since -3 does not contain the variable to solve for, move it to the right-hand side of the inequality by adding 3 to both sides.

4x<3-9

10. Subtract 9 from 3 to get -6.

4x<-6

11. Divide each term in the inequality by 4.

(4x)/(4)<-(6)/(4)

12. Simplify the left-hand side of the inequality by canceling the common factors.

x<-(6)/(4)

13. Simplify the right-hand side of the inequality by simplifying each term.

x<-(3)/(2)

14. The solution to the inequality includes both the positive and negative versions of the absolute value.

so the answer is x>3 or x<-(3)/(2)

First add subtract 2 to both side and get |4x-3| > 13

Now use the property: if |x| > a then x>a or x < -a

This results in: 4x-3 > 13 or 4x - 3 < -13

Now solve each one: 4x-3> 13 ==> 4x > 16 ==> x>4

4x-3 < -13 ==> 4x < -10 ==> x< - 5/2

Solution: x>4 or x < -5/2

|4x - 3| + 2 > 11

|4x - 3| + 2 - 2 > 11 - 2

|4x - 3| > 9

You have 2 cases to study.

First case : 4x - 3 is positive

4x - 3 > 9

4x - 3 + 3 > 9 + 3

4x > 12

x > 3

Second case : 4x - 3 is negative

- 4x + 3 > 9

- 4x + 3 - 3 > 9 - 3

- 4x > 6

- x > 6/4

x < - 3/2

Solution : x Є ] -∞ ; - 3/2 [ U ] 3 ; +∞ [

I'm French, excuse my language.