Module_07 // Language
ALGEBRAIC EXPRESSIONS
If an equation is a complete mathematical sentence, an expression is just a phrase. It has no equals sign. It is simply a collection of numbers, variables, and operators waiting to be organized.
Anatomy of an Expression
3CoefficientxVariable+5Constant
Coefficient
The number attached to the front of a variable. It multiplies the variable. (e.g., 3x means 3 times x).
Variable
A letter representing an unknown or changing number.
Constant
A standalone number. It has no variable attached, so its value never changes.
Like Terms
You can only add or subtract terms if they share the exact same variable. You can add apples to apples, but not apples to oranges!
YES
3x + 2x = 5xNO
3x + 2yInteractive Lab
Simplification Engine
Set the Value of 'x'2
Unsimplified Expression
3x+4+2x-1
3(2)+4+2(2)-1
6+4+4-1
= 13
Simplified Expression
5x+3
5(2)+3
10+3
= 13
Notice how both sides ALWAYS equal the exact same number, no matter what x is. Simplifying an expression just means doing the math early so there are fewer pieces to plug numbers into later!
English to Math Translation
Algebra often requires reading an English sentence and turning it into a mathematical expression.
- "5 more than a number"x + 5
- "Twice a number"2x
- "4 less than a number"x - 4
Verification Protocol
Knowledge Check: Terminology1 / 3
Which of the following is an EXPRESSION (not an equation)?
Rule Mastery
You can read, write, and simplify the language of math.