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>yx<y

x+z>y+zx+z<y+z

xz>yzxz<yz


Example

x+3>9

x+33>93

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

xz>yz

xz>yz

Ifz>0

When we multiply or divide an inequality by a negative integer, the sign of the inequality will be reversed (changed).

x>y

xz<yz

xz<yz

Ifz<0


Example

x23

x2232

x6


Video lesson

Solve the inequality

23x<14