- Topics At a Glance
- Expressions
- Addition
- Subtraction
- Multiplication
- Division
- Parentheses
- Variables
- Translating Slowly
- Equations and Inequalities
- The Equals Sign
- Inequalities
- Word Problems
- How to Read Word Problems
- How to Do Word Problems
- Geometry Problems
- Averages
- Percents
- The Word "Per"
- Coin Problems
- Written Inequalities
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem
Introduction to Inequalities:
We have four possible inequality signs to choose from: <, >, ≤, and ≥. There is also the slightly less popular ^, which means that everything below is greater than everything above, but that brings us into a touchy area, spiritually speaking. Translating English into one of these symbols is a matter of common sense. Good thing you have some of that.
The signs < and > are usually straightforward.
- "Three is less than x'' can be abbreviated by 3 < x.
- "5 is more than x'' can be written in symbols as 5 > x.
When we're translating into statements that use ≤ or ≥, we have a slightly wider range of English phrases to use. For example, each of the following English statements translates into symbols as x ≤ 20.
- x is less than or equal to twenty.
- x is at most twenty.
- x is not more than twenty.
- x is not greater than twenty.
- Twenty could be more than x, could be exactly as much as x. You'll never know. Na-nana-boo-boo.
Each of these following English statements translates into symbols as x ≥ 0.
- x is greater than or equal to zero.
- x is not less than zero.
- x is not smaller than zero.
- x is at least zero.
Inequalities Practice:
Translate the English sentence into a mathematical equation or inequality as appropriate:
Three y plus seven equals forty-two.
Translate the English sentence into a mathematical equation or inequality as appropriate:
Seven-eighths of x is at most thirty.
Translate the English sentence into a mathematical equation or inequality as appropriate:
Nine is less than y.
Translate the English sentence into a mathematical equation or inequality as appropriate:
Three less than one-fifth of y is eleven.
Translate the English sentence into a mathematical equation or inequality as appropriate:
z minus one is at least negative two.
Translate the English sentence into a mathematical equation or inequality as appropriate:
If we quadruple x and then add four we get eight.
Translate the English sentence into a mathematical equation or inequality as appropriate:
The ratio of x and four is greater than the difference of x and two.
Translate the English sentence into a mathematical equation or inequality as appropriate:
The total of x and five is no more than four.
Translate the English sentence into a mathematical equation or inequality as appropriate:
Three times z yields fifty-one.
Translate the English sentence into a mathematical equation or inequality as appropriate:
x combined with the difference of x and four yields three.
