Free ebook covering algebra basics, including variables, expressions, order of operations, and one-step and two-step equations.
Free ebook content
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Algebra Basics: Understanding Variables and Mathematical Language
+ Exercise: In the expression 3x₁ + x₂ - 10, which statement correctly identifies the variables, coefficients, and constant?
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Algebraic Expressions: Building and Reading Expressions with Variables
+ Exercise: Which expression correctly represents “the sum of x and 4 divided by 2”?
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Order of Operations in Algebra: Evaluating Expressions Correctly
+ Exercise: When evaluating the expression 18 ÷ 3x at x = 2, what is the correct way to interpret the operations before substituting and computing?
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Simplifying Expressions: Combining Like Terms and Using the Distributive Property
+ Exercise: Which simplified expression correctly results from distributing and combining like terms in: -2(3x - 5) + x - 4?
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From Words to Algebra: Translating Statements into Expressions and Equations
+ Exercise: Which algebraic expression correctly translates the phrase “5 less than a number” (let n be the number)?
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Equations and Solutions: What It Means to Solve for a Variable
+ Exercise: What does it mean for a number to be a solution to an equation with a variable?
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One-Step Equations: Using Inverse Operations to Isolate the Variable
+ Exercise: When solving a one-step equation, which action correctly uses an inverse operation to isolate the variable while keeping the equation balanced?
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Two-Step Equations: Combining Inverse Operations in the Right Order
+ Exercise: When solving a two-step equation like x/4 + 2 = 7, which sequence of inverse operations correctly isolates x?
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Algebra in Real-World Contexts: Modeling and Solving Simple Problems
+ Exercise: A taxi charges a $6 pickup fee plus $2 per mile. The total fare is $22. Which equation correctly models the situation to find the number of miles traveled?
About the free ebook
Algebra Basics: A Clear Start with Variables, Expressions, and Equations
Build a confident foundation in algebra with this free online ebook for school learners. It introduces the mathematical language used to describe unknown values, patterns, and relationships.
Learn how algebra works
Start by understanding variables, constants, coefficients, and operations. Practice reading and creating algebraic expressions, then evaluate them by substituting known values and applying the correct order of operations.
Make expressions easier to work with
Discover how to simplify expressions by combining like terms and using the distributive property. Clear examples show why terms can be combined only when they share the same variable part.
Turn language into mathematics
Learn to translate everyday statements into expressions and equations. This skill helps connect words such as more than, twice, and equal to with accurate algebraic notation.
Solve equations step by step
Explore what a solution means and use inverse operations to isolate a variable. The ebook progresses from one-step equations to two-step equations, emphasizing the importance of doing the same operation to both sides.
Use algebra beyond the classroom
Apply basic equations to simple real-world situations involving quantities, prices, totals, and unknown amounts. By the end, you will have practical methods for writing, simplifying, evaluating, and solving introductory algebra problems.
Key skills developed
- Identify variables and parts of expressions
- Evaluate and simplify algebraic expressions
- Translate verbal statements into equations
- Solve one-step and two-step equations
- Model simple real-world problems with algebra
What is the difference between an expression and an equation in algebra?
An expression has numbers, variables, and operations, while an equation states that two expressions are equal.
How do you combine like terms?
Add or subtract coefficients only when terms have the same variable and exponent, such as 3x and 5x.
What is the first step when solving a two-step equation?
Undo addition or subtraction first, then undo multiplication or division to isolate the variable.
This ebook includes:
9 content chapters
Digital certificate of course completion (Free)
Exercises to train your knowledge
100% free, from content to certificate
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