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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.)

 Oct 20, 2017

Best Answer 

 #1
avatar+7350 
+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

 

 Oct 20, 2017
edited by hectictar  Oct 20, 2017
 #1
avatar+7350 
+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

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