I find it easiest to learn from examples, so here are a few:
1) 5x + 3 > 7
5x > 4
x > 4/5
These are the easy ones haha
2) 0.7x + 2 > 19
0.7x > 17
x < 17/0.7
Note - if you're diving by a number that is a decimal, you need to flip the sign (i.e. > changes to < and < changes to >
. Loads of people always forget to do this.
3) x^2 + 4x + 3 > 0
Factorise to get (x+1)(x+3) > 0
Now draw the x^2 + 4x + 3 graph, which will be a positive parabola (aka a smiley face) since the x^2 term is positive and will cross the x-axis at -1 and -3, shown by the factorisation. As you want the area where the graph is above 0, you need either side of -1 and -3, so the answer is:
x < -3 or x > -1.
For quadratic inequalities, always draw the graph as it's the easiest way to find which area you want. If it's x^2 + ... > 0 you need the area above the x-axis, if it's x^2 + ... < 0 you need the area below the x-axis.
Hope that helped, if it didn't then let me know and I'll try again!