We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
67
1
avatar

What interval consists of all $w$ which satisfy ${\bf neither}$ $-2(6+2w)\le -16$ nor $-3w\ge 18$ ?

 Jul 13, 2019
 #1
avatar+8579 
+3

What interval consists of all \(w\) which satisfy \(\bf neither\) \(-2(6+2w)\le -16\) nor \(-3w\ge 18\) ?

 

 

If  w  makes the inequality   -2(6 + 2w) ≤ -16   false, then

it must make the inequality  -2(6 + 2w) > -16   true.


-2(6 + 2w)  >  -16

                             Divide both sides by  -2, a negative number, so flip the sign

6 + 2w  <  8

                             Subtract  6  from both sides of the inequality.

2w  <  2

                             Divide both sides by  2, a positive number, so don't flip the sign

w  <  1

 

If   -2(6 + 2w) > -16   then   w < 1

 

 

If  w  makes the inequality   -3w ≥ 18   false, then

it must make the inequality  -3w < 18   true.

 

-3w  <  18

                  Divide both sides by  3, a negative number, so flip the sign.

w  >  -6

 

If   -3w < 18   then   w > -6

 

 

So the solution to the question is all  w  such that   w < 1   and   w > -6

That is all  w  in the interval   (-6, 1)

 Jul 13, 2019

18 Online Users

avatar