Solve the inequality and express the solution in interval form.

Solution:

For convenience we'll compare an appropriate expression to 0 instead of 1. Then we can find x-values of interest to determine where to shade (i.e. where the inequality is true).

 





















This graph shows our solution another way. Notice that we graph both sides of the inequality. Then we can actually see when the left side is greater...

Solve the inequality: 3x/(x+2)<=1/(x+2)

 


 
points of interest: 
 and  

After checking the inequality on all three intervals we get 
 

Solve the inquality algebraically

Solution:


intervals of interest: 
(-oo,-2) , (-2, 2), (2,4), and (4, oo), why? 

Testing... 
if x=-3 then -7/5 is less than 0 
if x=0 then -4/-4 is not less than 0 
if x=3 then -1/5 is less than 0 
if x=5 then 1/21 is not less than 0 
so the solutions is 
(-oo,-2) U (2,4)

use the multiplication property of inequalities to solve the inquality .. negative 1 over 9 t is greater than or equal to 7 what is the solution set?

 
 
from which we uncover -1/63 and 0. After testing all three intervals we deduce that 

[-1/63, 0) 
is our solution 

:)

Solve the following inequality 60x-64 < 60/x

 


 



 
leads to these values of interest: 
,  or  
so that after testing on all intervals we find the solution interval: 
 or 

Solve the inequality and express the solution in interval form.

Solve the inequality and express the solution in interval form.