
You know how to solve an inequality (inequality solving, 7th Grade lesson).
Now instead of the sign =, there is either < or >.
You can solve this kind of inequality the same way as seen in the 7th Grade lesson.
The only difference is situated in the third example.
2x + 2 < 4
2x < 4  2
2x < 2
x < 2 ÷ 2
x < 1

9x  9 < 54
9x < 54 + 9
9x < 63
x < 63÷ 9
x < 7

3x + 3 < 6x + 6
3x  6x < 6  3
3x < 3
x > 3÷(3)
x > 1

Have you noticed? When you divide by a negative number, the inequality is reversed.
It’s the same thing if you multiply with a negative number.
For example, you have known since you were a child that 2<3 (at last something you understand!).
Multiply both sides by 10, it makes 20 and 30. It’s 30 which is the smallest, that's why you have to change the inequality sign (20>30).
2x + 4 > 4x  16
2x  4x > 16  4
2x > 20
x < (20)÷(2)
x < 10
A last example that you must understand and it will be OK.
See also : algebra on fmaths.com

