Answer:
C) x = 3
Step-by-step explanation:
To find the solution value that satisfies the inequality 4 < 3x∕2 + 1 < 7, you must plug every x value into the x and see which one works.
Plug 0 into x
4 < 3(0)∕2 + 1 < 7
4 < 0∕2 + 1 < 7
4 < 0 + 1 < 7
Combine like terms
4 < 1 < 7
This is false, 1 is not greater than 4.
Plug 4 into x
4 < 3(4)∕2 + 1 < 7
4 < 12∕2 + 1 < 7
4 < 6 + 1 < 7
Combine like terms
4 < 7 < 7
This is false, 7 is not less than 7.
Plug 3 into x.
4 < 3(3)∕2 + 1 < 7
4 < 9∕2 + 1 < 7
4 < 4.5 + 1 < 7
Combine like terms
4 < 5.5 < 7
This is true, 5.5 is greater than 4 and less than 7.
Plug 6 into x.
4 < 3(6)∕2 + 1 < 7
4 < 18∕2 + 1 < 7
4 < 9 + 1 < 7
Combine like terms
4 < 10 < 7
This is false, 10 is not less than 7.
C) x = 3 is the only true solution that works, so that is your answer.
I hope that helped and have a lovely rest of your day! :)