absolutes help show work

Question

Solve the absolute value inequality and write interval notation for the solution set. (show all work)

 

 

a) | 5 - 6x | ≥ 7

 

b) | 6x – 5 | < 9

 

 

Answer 1

Hi Theresa,

 

a)  abs value 5-6x≥7

 

5-6x≥7  or 5-6x≤-7

 

first inequality

 

5-6x≥7

 

-6x≥2

 

x≤-1/3

 

second inequality

 

5-6x≤-7

 

-6x≤-12

 

x≥2

 

The solutions are all real numbers less than equal to -1/3 or greater than equal to 2.

 

b) abs value 6x-5<9

 

-9<6x-5<9

 

-9+5<6x-5+5<9+5

 

-4<6x<14

 

-4/6<6x/6<14/6

 

-2/3<x<7/3