Solving inequalities
When we add or subtract the same number on both sides of the truth of the inequality doesn't change.
This holds true for all numbers:
$$x> y \to x< y \to$$
$$x+z> y+z\to x+z< y+z\to $$
$$x-z> y-z \to x-z< y-z\to$$
Example
$$x+3> 9$$
$$x+3-3> 9-3$$
$$x> 6$$
It is a little bit trickier when it comes to division and multiplication
When we multiply or divide an inequality by a positive integer, the truth of the inequality doesn't change.
$$x> y \to$$
$$x\cdot z> y\cdot z\to$$
$$\frac{x}{z}> \frac{y}{z}$$
$$If\; z> 0$$
When we multiply or divide an inequality by a negative integer, the sign of the inequality will be reversed (changed).
$$x> y \to$$
$$x\cdot z< y\cdot z\to$$
$$\frac{x}{z}< \frac{y}{z}$$
$$If\; z< 0$$
Example
$$\frac{x}{-2}\geq 3$$
$$\frac{x}{-2}\cdot -2\geq 3\cdot -2$$
$$x\leq -6$$
Video lesson
Solve the inequality
$$2-3x<14$$