Write the following in interval notation: − 4 < − 2 x − 14 < 3

Question

Write your solution using interval notation. If your answer contains fractions, please enter a fraction, decimal approximations will not be accepted.

Answer 1

This inequality can be solved in the following way (since the variable only occurs in the 'middle' portion).

 

− 4 < − 2 x − 14 < 3    divide all portions by -2, remembering to reverse the inequality symbols: 2 > x+7 >-3/2

Finally, subtract 7 in all three portions:  -5 > x > -8½

 

Same as Michael F's answer, of course.

Answer 2

− 4 < − 2 x − 14 < 3 This is really two inequalities.

-4<-2x-14   and   -2x-14<3

-4<-2x-14 multiply by -1 to get 4>2x+14 subtract 14 from each side to get -10>2x or 2x<-10 or x<-5

− 2 x − 14 < 3add 14 to each side to get -2x<17 divide by -2 to get x>-17/2

The interval in question is -17/2<x<-5

=(-17/2,-5)