Solve the following inequality algebraically:
[tex]$-2\ \textless \ \frac{x}{3}+1\ \textless \ 5$[/tex]
A. [tex]$-9\ \textgreater \ x\ \textgreater \ 12$[/tex]
B. [tex]$-9\ \textless \ x\ \textless \ 12$[/tex]
C. [tex]$-2\ \textless \ x\ \textless \ 5$[/tex]
D. [tex]$-2\ \textgreater \ x\ \textgreater \ 5$[/tex]
Please select the best answer from the choices provided.
Answer (2)
Subtract 1 from all parts of the inequality: − 3 < 3 x < 4 .
Multiply all parts of the inequality by 3: − 9 < x < 12 .
The solution to the inequality is − 9 < x < 12 .
The correct answer is B: $\boxed{-9
The solution to the inequality − 2 < 3 x + 1 < 5 is − 9 < x < 12 , which corresponds to option B. This was determined by solving the two parts of the inequality separately. Hence, the correct answer is B.
;
