Graph the Solution Set

Question

6X+3

------ < -3 

-5 

Answer 1

(6X + 3) / (-5)  <  -3  

 

First multiply both sides of the inequality by (-5).  Remember that when you multiply or divide an inequality by a negative number you must reverse the direction of the inequality  

 

6X + 3 > 15

 

Next subtract 3 from both sides and then divide both sides by 6  

 

6X > 12

 

X > 2  

 

To graph this on a number line, put an open circle around the point 2 (because 2 is not included in the solution set) and then shade everything to the right of 2 with an arrow to the right indicating that the shading goes on indefinitely  

 

To check the solution, try picking a value to the right of 2 (like 7) and plug it in to the original inequality to see if it works

 

(6*7 + 3) / (-5) = 45 / (-5) = -9, which checks since it is less than (-3)  

 

Also pick a value to the left of 2 (like -2) to make sure it does not satisfy the inequality  

 

(6*(-2) + 3) / (-5) = (-15) / (-5) = 3, which checks since it is not less than (-3)  

 

Finally, you can check the boundary point (2) which should result in both sides being equal  

 

(6*2 + 3) / (-5) = 15 / (-5) = -3, which does result in equality.  Note that (2) is not part of the solution set since it is a strict inequality