19 topics
Algebra help, worked out step by step
Most algebra trouble is not really about algebra. It is about a rule that was memorised without its reason — why you can multiply both sides but not add across a fraction, why x = ±3 has two answers and √9 has one. Once the reason lands, the manipulation stops feeling arbitrary and starts feeling forced.
Where students get stuck
I factor by guessing and it takes forever
Guess-and-check works until the leading coefficient stops being 1. The reliable method is to multiply a by c, find the pair of factors of that product which add to b, split the middle term into those two pieces, and factor by grouping. It is four mechanical steps with no guessing, and it works on every trinomial that factors at all — including the ones where guessing burns ten minutes.
Why does the inequality sign flip?
Because multiplying by a negative reverses order on the number line. 2 < 5 is true; multiply both sides by −1 and −2 < −5 is false, so the sign has to flip to −2 > −5. This is the single most common lost mark in an inequalities unit, and it is not a rule to memorise — it is what negation does to order.
I lose solutions, or I get answers that don't work
Two different errors that look the same on a report card. Dividing both sides by a variable loses the solution where that variable is zero — factor instead. Squaring both sides invents solutions that were never there, which is why every radical equation needs its answers substituted back in. Extraneous roots are not a mistake in your algebra; skipping the check is.
Word problems — I can't get started
The stall is almost always at the first line, not the algebra. Name the unknown explicitly in writing ('let t = hours after 2pm'), write the one sentence in the problem that is an equality, then translate that sentence and nothing else. Most word problems contain exactly one such sentence, and it is usually the one with 'total', 'is', or 'same' in it.
What's covered
Algebra topics you can work through with a tutor, generate practice on, or turn into flashcards and a study plan.
Expressions and equations
- Order of operations and sign rules
- Linear equations in one variable
- Literal equations and rearranging formulas
- Absolute value equations and inequalities
- Compound inequalities and interval notation
Polynomials and factoring
- Laws of exponents
- Expanding and the special products
- Common factoring and factoring by grouping
- Trinomials with a leading coefficient
- Difference of squares and sum/difference of cubes
Quadratics
- Solving by factoring, completing the square, and the quadratic formula
- The discriminant and the number of real roots
- Vertex form and graph transformations
- Word problems: projectiles, area, and revenue
Rationals, radicals, and systems
- Simplifying rational expressions and restrictions
- Adding rational expressions with unlike denominators
- Radical equations and extraneous roots
- Systems by substitution and elimination
- Systems of linear inequalities
Algebra questions
Will it just give me the answer to my algebra homework?
No. It works the problem out on the whiteboard one step at a time and asks you what comes next. If you want the answer checked rather than taught, you can paste your own attempt and it will tell you which line the error is on instead of redoing it for you.
Can I take a photo of the textbook page instead of typing the equation?
Yes. You can hold the page up to your camera or share your screen, and the tutor reads the question off it. Typing algebra notation is the slowest part of getting help, so most students never do it.
I have a test on quadratics on Friday. What should I actually do?
Generate a practice quiz on quadratics, work it, and let it grade you. The quiz comes back with full worked solutions rather than a score, so the questions you got wrong become the study session. Anything still shaky after that is what you talk through out loud.
Stuck on algebra right now?
Talk it through out loud, share your screen, and watch it worked out step by step on a whiteboard.
Start free — no card