Did I work this correctly?

Question

2 < 2x - 1 < 7

I got x < 4.

Right or wrong?

Answer 1

You solved 2x-1 < 7 correctly.

but think about ALL numbers less than four (like negative one billiion!) Will they all make 2x -1 greater than 2? No.

(this is how you can check your own answers to see if they are reasonable. If your solution is a one sided inequality, try an "extreme' example to see if it still works.)

so you need to also find x 's which are also solutions to
2 < 2x -1.

the previous posters show how to solve both inequalities at the same time.

Answer 2

Wrong.

2 < 2x - 1 < 7
3<2x<8
1.5

Answer 3

add 1 to all 3 slots
3<2x<8
divide 2 on all 3 slots
3/2