I do not believe the Bible that much but thank you for your blessing! I love to help even if I am just a holy Heathen.
3(x-4) > 7x-9
You can manipulate this one just like an equation
There is one rule that is different in balancing inequalities and equations
When you divide or multiply both sides of an inequality, and the multiplier is less than zero, then the direction of the inequality changes.
For example 1 < 2 but if you multiply both sides by -2 it becomes: -2 > -4.
It is as if you took the whole number line with the + and numbers on it and flipped it around backwards and then stretched it.
But this one is so simple you don't even have to know that
3(x-4) is always 3x - 12
3x - 12 > 7x - 9 Remember we are trying to discover what values of x will work and make this true.
Add 9 to each side
3x - 3 > 7x
Subtract 3x from each side
-3 > 4x
Divide both sides by 4
-3/4 > x
I always understand these better if the x is on the left. Let me do it again in a different order
3x - 12 > 7x - 9
Subtract 7x and add 12 to each side
-4x > 3
Divide by -4
x < -3/4
Now graph it. Here is a number line I am trying to type you from -2 to +2
and I am shading it with #### and a O for the endpoint which is open.
I hope you can see here that I am making fractions like this
1
1/2 is --
2
|---+---+---+---|---+---+---+---|---+---+---+---|---+---+---+---|
-7 -3 -5 -3 -1 -1 1 1 3 5 3 7
-2 -- -- -- -1 -- -- -- 0 -- -- -- 1 -- -- -- 1
4 2 4 4 2 4 4 2 4 4 2 4
<###+####+###+###|###O---+---+---|---+---+---+---|---+---+---+---|
-7 -3 -5 -3 -1 -1 1 1 3 5 3 7
-2 -- -- -- -1 -- -- -- 0 -- -- -- 1 -- -- -- 1
4 2 4 4 2 4 4 2 4 4 2 4