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→x<y→
x+z>y+z→x+z<y+z→
x−z>y−z→x−z<y−z→
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→
x⋅z>y⋅z→
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→
x⋅z<y⋅z→
xz<yz
Ifz<0
Example
x−2≥3
x−2⋅−2≥3⋅−2
x≤−6
Video lesson
Solve the inequality
2−3x<14