In real life, inequalities are probably used most often when comparing resources with various requirements.

Example

I have some money and my wife has $11. We would like to attend a dance that will cost us $12. How much money must I have if we are to gain admission to the dance?

x + 11 ≥ 12 (formulate the problem--our money must exceed the admission cost)

x ≥ 12-11 (solve by subtracting 11 from both sides)

x ≥ 1

I need to have $1 or more. (interpret results)

(It worked out that I had $7 and my wife actually had $12. She paid, and we danced 'til we dropped.)

Example

I have some money and my wife has $11. We would like to attend a dance that will cost us $12. How much money must I have if we are to gain admission to the dance?

x + 11 ≥ 12 (formulate the problem--our money must exceed the admission cost)

x ≥ 12-11 (solve by subtracting 11 from both sides)

x ≥ 1

I need to have $1 or more. (interpret results)

(It worked out that I had $7 and my wife actually had $12. She paid, and we danced 'til we dropped.)