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
x > 2.85
For solving the inequality, we'll move 4x to the left side and the free term to the right side:
In order to do the calculations, we'll have to have the same denominator, which is 2. For this reason, we'll amplify each term, except the ratio (1/2)x, with 2.
We'll multiply with (-1) and the direction of inequality will be changed:
x belongs to the set (20/7, +inf)