+0  
 
0
48
1
avatar+101 

Solve the inequality. Give the solution set in both interval and graph forms.

 

StartFraction 2 k minus 5 Over negative 6 EndFraction greater than 52k−5−6 > 5

 

2k - 5  > 5 

-6 

 

(I have (- , - 25)

                        2

 

( symbol shaped like an eight goes before the   ,-

 

The solution set in interval notation is _________.

(Type your answer in interval notation. Simplify your answer. Use integers or decimals for any numbers in the  expression.)

ladiikeiii  Oct 20, 2017

Best Answer 

 #1
avatar+5227 
+2

(2k - 5) / (-6)    >    5

                                     Multiply both sides of the inequality by  -6  .

                                     Since we are multiplying by a negative, also flip the inequality sign .

2k - 5   <   5 * -6

2k - 5   <  -30

                            Add  5  to both sides.

2k   <  -30 + 5

2k   <  -25

                           Divide both sides by  2  . (2 is positive, so the sign stays the same.)

k   <   -25 / 2

 

In interval notation, the solution set should be:  (-∞, -25/2)

 

Ah! Now I see what is "wrong" with your answer....

"Use integers or decimals for any numbers in the  expression."

 

So just turn  -25/2  into  -12.5  and we have...    (-∞, -12.5)

 

And the number line looks roughly like this

 

hectictar  Oct 20, 2017
edited by hectictar  Oct 20, 2017
Sort: 

1+0 Answers

 #1
avatar+5227 
+2
Best Answer

(2k - 5) / (-6)    >    5

                                     Multiply both sides of the inequality by  -6  .

                                     Since we are multiplying by a negative, also flip the inequality sign .

2k - 5   <   5 * -6

2k - 5   <  -30

                            Add  5  to both sides.

2k   <  -30 + 5

2k   <  -25

                           Divide both sides by  2  . (2 is positive, so the sign stays the same.)

k   <   -25 / 2

 

In interval notation, the solution set should be:  (-∞, -25/2)

 

Ah! Now I see what is "wrong" with your answer....

"Use integers or decimals for any numbers in the  expression."

 

So just turn  -25/2  into  -12.5  and we have...    (-∞, -12.5)

 

And the number line looks roughly like this

 

hectictar  Oct 20, 2017
edited by hectictar  Oct 20, 2017

16 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details