Match each double inequality with its solution

Question

double inequality's:

1. -2<-3x+7<10

2. -11<-4x-3<1

3. -3<x+5<11

4. -10<-5x+10<5

5. -10<5x+15<5

solutions:

A. -1<x<2

B. -5<x<-2

C. -1<x<3

D. 1<x<4

E. -8<x<6

Answer 1

I'll do the first one for you.  You can do the rest following the same procedure.

 

     -2 < -3x + 7 < 10

 

Subtract 7 from all three sides:

 

     -2 - 7 < -3x + 7 - 7 < 10 - 7

    -9 < -3x < 3

 

Now divide all three sides by -3.  Remember that when you multiply or divide an inequality by a negative number, you flip the inequality signs

 

     -9/(-3) > -3x/(-3) > 3/(-3)

     3 > x > -1  which is the same as -1 < x < 3

 

The answer is C.