1 2 x + 3

Solve inequalities is no different than solving regular equations.  In both cases, you need to get all the x terms on one side of the equation and all the numbers on the other.

One way to do this question is this:

Subtract 4x from both sides.  You now have

-3.5x + 3 < -7

Subtract 3 from both sides

-3.5x < -10

Divide both sides by -3.5.  Be sure to switch the direction of the inequality sign.

x > 2.85

If you prefer, you can multiply both sides by 2 to get your .5x to be x.

x + 6 < 8x - 14

Then you move the 8x and the 6.

-7x < -20

Again, be sure to switch the direction of the inequality sign.

x > 20/7

or

x > 2.85