[tex]1 < 4x + 2 < 10[/tex]
First let's subtract 2 from everything in the inequality:
[tex]1 - 2 < 4x + 2 - 2 < 10 - 2[/tex]
[tex]-1 < 4x < 8[/tex]
Next, let's divide 4 from everything in the inequality:
[tex]\frac{-1}{4} < \frac{4x}{4} < \frac{8}{4}[/tex]
[tex]\frac{-1}{4} < x < 2[/tex]
This is the final solution to the inequality: [tex](\frac{-1}{4}, 2)[/tex]
