R E B O OT C O M PU T E R S E RVI C ES I N C . · C O L L E G E ST U DY S E R I ES
Algebra 101
The Complete Study Guide to College Algebra
Rules · Worked Examples · Practice Problems + Solutions
Inside this guide
1 · The Language of Algebra
2 · Solving Linear Equations & Inequalities
3 · Exponents, Radicals & Polynomials
4 · Factoring
5 · Quadratic Equations
6 · Functions & Graphing
7 · Systems of Equations
8 · Master Formula Sheet
9 · 20 Practice Problems with Full Solutions
10 · Glossary of Key Terms
A self-study companion for college algebra · rebootcs.com
, 1 · The Language of Algebra
Algebra is arithmetic with letters. A variable is a symbol (like x) standing for an unknown number; a constant is a fixed
value. A term is a number, a variable, or a product of them; an expression is terms combined with + and −.
Order of Operations (PEMDAS)
Parentheses → Exponents → Multiplication/Division (left to right) → Addition/Subtraction (left to right).
WORKED EX AMPLE 1.1
Evaluate 3 + 4 × 2² − (5 − 1).
Solution. Parentheses: (5−1)=4. Exponent: 2²=4. Multiply: 4×4=16. Now 3 + 16 − 4 = 15.
Properties You Will Use Constantly
Property Statement
Commutative a + b = b + a; ab = ba
Associative (a+b)+c = a+(b+c)
Distributive a(b + c) = ab + ac
Identity a + 0 = a; a × 1 = a
Inverse a + (−a) = 0; a × (1/a) = 1
© Reboot Computer Services Inc. · Created by Mario Washington · Page 2 of 12
Algebra 101
The Complete Study Guide to College Algebra
Rules · Worked Examples · Practice Problems + Solutions
Inside this guide
1 · The Language of Algebra
2 · Solving Linear Equations & Inequalities
3 · Exponents, Radicals & Polynomials
4 · Factoring
5 · Quadratic Equations
6 · Functions & Graphing
7 · Systems of Equations
8 · Master Formula Sheet
9 · 20 Practice Problems with Full Solutions
10 · Glossary of Key Terms
A self-study companion for college algebra · rebootcs.com
, 1 · The Language of Algebra
Algebra is arithmetic with letters. A variable is a symbol (like x) standing for an unknown number; a constant is a fixed
value. A term is a number, a variable, or a product of them; an expression is terms combined with + and −.
Order of Operations (PEMDAS)
Parentheses → Exponents → Multiplication/Division (left to right) → Addition/Subtraction (left to right).
WORKED EX AMPLE 1.1
Evaluate 3 + 4 × 2² − (5 − 1).
Solution. Parentheses: (5−1)=4. Exponent: 2²=4. Multiply: 4×4=16. Now 3 + 16 − 4 = 15.
Properties You Will Use Constantly
Property Statement
Commutative a + b = b + a; ab = ba
Associative (a+b)+c = a+(b+c)
Distributive a(b + c) = ab + ac
Identity a + 0 = a; a × 1 = a
Inverse a + (−a) = 0; a × (1/a) = 1
© Reboot Computer Services Inc. · Created by Mario Washington · Page 2 of 12
