Algebra Topics Covered at Every Level
Algebra is the foundation for nearly every math course that follows it. Tutors adapt their explanations to your course, so tell them whether you are in pre-algebra, Algebra 1, Algebra 2, honors algebra, college algebra or linear algebra.
Pre-Algebra
- Integers, fractions, decimals and the order of operations
- Variables, expressions and one-step and two-step equations
- Exponents, square roots and powers
- Prime factorization of natural numbers, ratios and percentages
Algebra 1
- Solving linear equations and inequalities
- Slope, intercepts and graphing lines
- Systems of equations by graphing, substitution and elimination
- Exponent rules, polynomials and factoring
- Radical and rational expressions
- Functions, domain and range, and an introduction to quadratics
Algebra 2 and Honors Algebra
- Quadratic functions, completing the square and complex numbers
- Polynomial and rational functions and their graphs
- Exponential and logarithmic functions and equations
- Sequences and series
- Matrices and systems with three variables
- Conic sections and radical equations
College Algebra
College algebra revisits many Algebra 2 topics with more depth and speed: functions and their transformations, inverse functions, logarithmic and exponential models, systems of equations and matrices, conic sections, and sequences. If your course moves into trigonometry and limits, our precalculus homework help page picks up from there.
Linear Algebra and Abstract Algebra
Linear algebra studies systems of linear equations and their transformation properties, including matrices, vectors, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors. It is used well beyond math, in least-squares fitting, solving coupled differential equations and describing rotations in space for engineering and physics. Abstract algebra, also called modern algebra, studies structures such as groups, rings and fields and is mostly proof-based.
Financial Algebra and Curriculum Programs
Financial algebra applies algebraic models to compound interest, loans, investments and budgeting. Students in structured programs such as CPM work through layered, team-based problem sets that build each idea across several lessons. Our CPM homework help page covers that program in more detail.
Why Algebra Homework Gets Difficult
Most students who struggle with algebra are not bad at math. They usually hit one of these obstacles:
- Gaps in the foundations. Trouble with fractions, negative numbers or exponents shows up again in every later topic.
- Abstract symbols. Letters stand for unknown numbers, functions and parameters, and it takes practice to read expressions fluently.
- One small error ruins the answer. A dropped negative sign early on carries through every line that follows.
- Too many rules. Exponent rules, log rules, factoring patterns and formulas pile up, and applying the wrong one gives a wrong answer even when the arithmetic is right.
- Word problems. Translating a paragraph into an equation is often harder than solving the equation itself.
Worked Examples: Step-by-Step Algebra Solutions
Here is how a tutor's solution walks through two common problem types.
A linear equation. To solve 4(x + 3) = 2x − 6, first distribute to get 4x + 12 = 2x − 6. Subtract 2x from both sides to collect the variable terms: 2x + 12 = −6. Subtract 12 from both sides: 2x = −18. Divide by 2: x = −9. Finally, check by substituting back. The left side is 4(−9 + 3) = −24 and the right side is 2(−9) − 6 = −24, so the answer is correct.
A quadratic equation. To solve x² − 5x + 6 = 0, look for two numbers that multiply to 6 and add to −5. Those are −2 and −3, so the equation factors as (x − 2)(x − 3) = 0. By the zero product property, x = 2 or x = 3. When a quadratic does not factor neatly, the quadratic formula works every time, and the discriminant, b² − 4ac, tells you in advance whether to expect two real solutions, one or none. Our guide on how to solve quadratic equations compares factoring, completing the square and the formula.
For systems, a solution should state which method it uses and why. Elimination is often fastest when coefficients line up, while substitution is simpler when one variable is already isolated. Our guide to solving systems of linear equations walks through both.
Common Algebra Mistakes to Watch For
- Distributing a negative sign. In −(x − 4), the result is −x + 4, not −x − 4.
- Squaring a sum. (a + b)² equals a² + 2ab + b², not a² + b².
- Flipping inequalities. When you multiply or divide both sides of an inequality by a negative number, the inequality sign reverses.
- Canceling terms instead of factors. In a rational expression you can cancel common factors, never individual terms that are added or subtracted.
- Dividing by a variable. Dividing both sides by x can lose the solution x = 0. Factor instead.
- Skipping the check. Radical and rational equations can produce extraneous solutions, so substitute every answer back into the original equation.
- Misusing log rules. The log of a sum is not the sum of the logs. The product rule applies to log(ab), not log(a + b).
How to Get Algebra Homework Help Online
- Post your assignment. Choose math as the subject, upload the problems or a clear photo or screenshot, and list your course, textbook and any method your teacher requires. Set your deadline and budget.
- Compare bids from math tutors. Tutors send bids. Review their profiles, ratings and reviews, and chat with them to ask how they would approach your problems.
- Pay and track progress. Pay for the bid you choose, follow the order and message your tutor if you have questions or extra instructions.
- Download and review. Download the step-by-step solutions, check them against your instructions and request a revision if anything is unclear or missing.
Support is available through live chat and at support@acemyhomework.com.
What a Good Algebra Solution Includes
- Every step written out, with a short reason for each one, such as "add 6 to both sides" or "factor out the greatest common factor"
- Notation and methods that match your textbook and teacher
- Answers checked by substitution, with extraneous solutions identified and discarded
- Graphs or tables where the problem asks for them, with axes and key points labeled
- For word problems, a clear definition of each variable and the equation built from the problem statement
Free Algebra Help vs. Working With a Tutor
Free help is a great first step. Worked examples in your textbook, answers to odd-numbered exercises, your teacher's office hours, classmates and study groups, and online calculators that show steps can resolve many questions. The limits appear with harder work. A calculator solves the equation you type, but it cannot tell you that you set up a word problem incorrectly, and it may not use the method your teacher expects. Textbooks are thorough but slow when a deadline is close.
A tutor helps when you need explanations tied to your assignment, when you keep making the same mistake and cannot see why, or when you are working on college algebra and linear algebra topics that general resources cover only briefly. For other math courses, see our main math homework help page.
Tips for Doing Algebra Homework on Your Own
- Set up a focused space. Keep your notes, calculator and textbook within reach, and silence your phone and social media.
- Read the problem twice. Make sure you know what is being asked before you start. If the instructions are unclear, ask your teacher or a classmate.
- Work one assignment at a time. Give each problem set your full attention instead of switching back and forth.
- Write every step. Skipping steps is the most common source of sign and arithmetic errors.
- Check your answers. Substitute solutions back into the original equation or test a point on your graph.
- Keep a rules sheet. Collect exponent rules, factoring patterns and formulas in one place as you learn them.
Need help with tonight's problem set? Post your algebra assignment, compare tutor bids and choose the expert whose explanations make the most sense to you.
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