[tex]5.1(3 + 2.2x) \ \textgreater \ -14.25 - 6(1.7x + 4)[/tex]
Lets expand both multiplications first.
[tex]15.3 + 11.22x \ \textgreater \ -14.25 - 10.2x - 24[/tex]
Simplify down the right side.
[tex]15.3 + 11.22x \ \textgreater \ -38.25 - 10.2x[/tex]
Add 38.25 to both sides.
[tex]53.55 + 11.22x \ \textgreater \ -10.2x[/tex]
Subtract 11.22x from both sides.
[tex]53.55 \ \textgreater \ -21.42x[/tex]
Divide by -21.42 on both sides. Because we're dividing by a negative, we need to change the inequality direction.
[tex]-2.5 \ \textless \ x[/tex]
This means, out of the options available, (-2.5, ∞) is the correct answer.
