How do you solve algebra equations with variables on both sides?

Use inverse operations to move variable terms to one side and constants to the other, then isolate the variable.

What is the difference between combining like terms and multiplying polynomials?

Combining like terms adds or subtracts terms with identical variables and exponents; multiplying polynomials uses distribution to create new terms.

How do inequality symbols affect a graph on a number line?

Use an open circle for and a closed circle for ≤ or ≥. Shade left for values less than and right for values greater than.

Free online course Algebra

Duration of the online course: 3 hours and 18 minutes

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Build algebra skills fast with a free online course: master equations, polynomials and inequalities through clear lessons and practice exercises.

In this free course, learn about

Multiply/divide real numbers; determine sign rules for products and quotients
Apply order of operations (PEMDAS) to simplify numerical and algebraic expressions
Find opposites and absolute values; interpret absolute value as distance from zero
Combine like terms, including multivariable terms and higher-degree terms
Solve linear equations using addition/subtraction to isolate the variable
Solve linear equations using multiplication/division; use inverse operations
Solve multi-step equations with distribution, parentheses, and variables on both sides
Translate word statements into equations and solve for unknowns
Solve and graph basic inequalities; understand open/closed circles and shading
Solve and graph compound inequalities using AND/OR; interval notation concepts
Use exponent rules and evaluate expressions with powers (e.g., squares and cubes)
Define polynomials; add and subtract polynomials by combining like terms
Multiply polynomials: monomial-by-polynomial, binomials (FOIL), and larger products
Use special products (difference of squares, squaring binomials) and solve polynomial equations

About the free online course

Strengthen your math foundation and gain confidence with algebra by learning how to reason step by step, not just memorize rules. This free online course is designed for students and anyone who wants a reliable refresher, turning confusing symbols and rules into a set of practical tools you can apply to homework, exams, and real-life problems.

You will begin with the essentials of working with real numbers, including how signs affect multiplication and division, and how to avoid common mistakes by using the order of operations correctly. From there, you will build comfort with opposite numbers and absolute value so you can interpret expressions accurately and simplify with confidence. As the course progresses, you will develop fluency in simplifying algebraic expressions by combining like terms, a key skill for nearly every topic that follows.

Next, you will learn how to solve equations systematically. You will practice isolating variables using addition and subtraction, then extend those ideas to multiplication and division, and finally to multi-step equations. You will also handle situations with variables on both sides, learning to keep your work organized and your logic consistent. To connect algebra to everyday thinking, you will translate word problems into equations, identify what the unknown represents, and choose efficient solution steps.

You will then move into inequalities, learning how solutions are represented on a number line and how different symbols change the meaning of a statement. By working with compound inequalities, you will see how to describe ranges of values clearly and how to graph them correctly. The course also introduces exponents and helps you build a strong sense of structure so expressions look less intimidating and more predictable.

Finally, you will develop core algebra skills with polynomials: adding and subtracting, multiplying by monomials, multiplying binomials and polynomials, and recognizing special products. You will apply these skills to polynomial equations and even to geometry contexts, reinforcing that algebra is a language for describing relationships and solving problems. With short videos and targeted exercises, you will get the repetition you need to improve accuracy, speed, and understanding.

Course content

Video class: Algebra Tutorial - 1 - Multiplying and Dividing Real Numbers 09m
Exercise: What is the result of multiplying a negative number and a positive number?
Video class: Algebra Tutorial - 2 - Order of Operations 07m
Exercise: What is the order of operations?
Video class: Algebra Tutorial - 3 - Opposite and Absolute Values 04m
Exercise: What is the absolute value of -25?
Video class: Algebra Tutorial - 4 - Combining Like Terms 05m
Exercise: What is the final result of combining like terms in the expression: 5y²x + 8y²x - 2x²y - x²y + 2xy + 3xy?

Video class: Algebra Tutorial - 5 - Solving Equations with Addition and Subtraction 06m
Exercise: What is the first step to solve an equation with addition and subtraction?
Video class: Algebra Tutorial - 6 - Solving Equations with Multiplication and Division 04m
Exercise: What operation is used to isolate the variable X in the equation 2X = 12?
Video class: Algebra Tutorial - 7 - Solving Combined Equations 04m
Exercise: What is the first step in solving the equation 7(x+2)=-35?
Video class: Algebra Tutorial - 8 - Solving Equations with Variables on Both Sides 05m
Exercise: What is the solution for x in the equation 3x - 2 = 4?
Video class: Algebra Tutorial - 9 - Solving Word Problems with Equations 07m
Exercise: What is the equation that represents the statement "the sum of twice a number and 21 is 83"?

Video class: Algebra Tutorial - 10 - Solving and Graphing Basic Inequalities 09m
Exercise: How does graphing inequalities work with different inequality symbols?
Video class: Algebra Tutorial - 11 - Solving and Graphing Compound Inequalities 07m
Exercise: What is a compound inequality?
Video class: Algebra Tutorial - 12 - Exponents 06m
Exercise: What is the product of 2 squared and 3 cubed multiplied by 4?

Video class: Algebra Tutorial - 13 - Adding and Subtracting Polynomials 06m
Exercise: What is a polynomial?
Video class: Algebra Tutorial - 14 - Multiplying a Polynomial by a Monomial 07m
Exercise: What is the correct result when multiplying -3x by the expression (6x - 5 + x)?
Video class: Algebra Tutorial - 15 - Multiplying Binomials 04m
Exercise: What is the result of multiplying the binomials (2x + 3) and (4x + 5)?
Video class: Algebra Tutorial - 16 - Multiplying Polynomials 07m
Exercise: When multiplying polynomials, what is one of the key differences compared to multiplying binomials?
Video class: Algebra Tutorial - 17 - Special Products of Binomials 03m
Exercise: What is the result of multiplying (X + 3) and (X - 3)?
Video class: Algebra Tutorial - 18 - Squaring Binomials 03m
Exercise: What is the result of squaring the binomial (a + b)?
Video class: Algebra Tutorial - 19 - Polynomial Equations 06m
Exercise: What is the value of X in the equation 4x - 2 = 3x - 6 + 10?
Video class: Algebra Tutorial - 20 - Solving Geometry Problems with Polynomials 07m
Exercise: What is the perimeter of a rectangle in terms of Y?
Video class: Algebra Tutorial - 21 - Solving Word Problems with Polynomials 08m
Exercise: What is the hardest part about solving word problems using polynomials?

Video class: Algebra Tutorial - 22 - Greatest Common Factor 09m
Video class: Algebra Tutorial - 23 - Factoring the Difference of Squares 06m
Exercise: What is a difference of squares equation?
Video class: Algebra Tutorial - 24 - Factoring Perfect Square Trinomials 04m
Video class: Algebra Tutorial - 25 - Factoring Trinomials 06m
Exercise: What is the process of factoring a normal trinomial?
Video class: Algebra Tutorial - 26 - Solving Equations- Factoring 06m
Video class: Algebra Tutorial - 27 - Factoring- Word Problems 06m
Exercise: What is the sum of the squares of two consecutive positive even integers if the sum is equal to 340?
Video class: Algebra Tutorial - 28 - Factoring- Geometry Problems 06m

Video class: Algebra Tutorial - 29 - Dividing Monomials 03m
Exercise: What is the result of dividing 18X^6Y by -3XY^5?
Video class: Algebra Tutorial - 30 - Dividing a Polynomial by a Monomial 04m
Video class: Algebra Tutorial - 31 - Simplifying Fractions 04m
Video class: Algebra Tutorial - 32 - Multiplying Fractions 04m

Learn aboutAlgebra basics

Explore free online Algebra basics courses designed to build confidence in equations, expressions, variables, inequalities, functions, and more. Learn at your own pace with beginner-friendly lessons, strengthen essential math skills, and earn a certificate upon completion. Start learning Algebra basics online for free today.