The short answer
An algebra solver with steps shows the whole route to the answer: each line of working, the rule that justifies it, and a check at the end. Scan the equation with Socratic Solve and you get the solution written out line by line: which rule is applied, what it does to the equation, and how it leads to the next line, all in real rendered notation. It works for typed questions too, but the camera is faster for anything with fractions, exponents or matrices.
Below are four fully worked examples showing what good step-by-step working looks like, the mistakes that cost the most marks, and how to read a solution so you learn the method instead of copying the answer.
Example: what an algebra solver with steps actually shows
Take a real exam question: given x = log₈(4y + 9), solve for y. An answer-only tool prints the result. A solver with steps shows the route:
- Rewrite the logarithm using the change-of-base formula: x = log(4y + 9) / log(8).
- Multiply both sides by log(8): x·log(8) = log(4y + 9).
- Exponentiate to undo the log: 10^(x·log 8) = 4y + 9. Since 10^(x·log 8) is the same as 8^x, this is 8^x = 4y + 9.
- Isolate y: y = (8^x − 9) / 4.
Each of those moves is a rule you'll reuse on every log problem this semester. That's the point of steps: the answer expires with question 3(a); the method carries the whole topic.
Four worked algebra examples, with steps
These are the problem types that show up on almost every algebra worksheet. Try each one on paper first, then compare your lines to these.
1. Linear equation: 3(x − 4) − 2 = 5x + 6
- Distribute: 3x − 12 − 2 = 5x + 6.
- Combine like terms: 3x − 14 = 5x + 6.
- Collect x on one side (subtract 5x from both sides): −2x − 14 = 6.
- Move the constant (add 14 to both sides): −2x = 20.
- Divide by −2: x = −10.
Check: left side 3(−10 − 4) − 2 = −42 − 2 = −44. Right side 5(−10) + 6 = −44. Both sides match, so x = −10 is correct.
2. Quadratic by factoring: x² − 5x − 14 = 0
- Find two numbers that multiply to −14 and add to −5: that's −7 and 2.
- Factor: (x − 7)(x + 2) = 0.
- Zero product rule: x − 7 = 0 or x + 2 = 0, so x = 7 or x = −2.
Check: 7² − 5(7) − 14 = 49 − 35 − 14 = 0, and (−2)² − 5(−2) − 14 = 4 + 10 − 14 = 0. A quadratic usually has two answers; losing one is a common way to drop a mark.
3. Quadratic by formula: 2x² + 3x − 4 = 0
This one doesn't factor nicely, so use x = (−b ± √(b² − 4ac)) / 2a with a = 2, b = 3, c = −4.
- Discriminant first: b² − 4ac = 9 − 4(2)(−4) = 9 + 32 = 41. It's positive, so there are two real roots.
- Substitute: x = (−3 ± √41) / 4.
- Decimal values: x ≈ 0.851 or x ≈ −2.351.
Working out the discriminant as its own line is worth the extra step: it's where most sign errors happen (−4 × 2 × −4 is plus 32), and it tells you how many solutions to expect before you finish.
4. System of equations: 2x + 3y = 12 and x − y = 1
- Rearrange the simpler equation: x = y + 1.
- Substitute into the other: 2(y + 1) + 3y = 12.
- Simplify: 5y + 2 = 12, so 5y = 10 and y = 2.
- Back-substitute: x = 2 + 1 = 3.
Check both equations: 2(3) + 3(2) = 12 and 3 − 2 = 1. A solution to a system has to satisfy every equation, not just the one you used last.
Bonus: a log equation with a trap
Solve log₂(x) + log₂(x − 2) = 3.
- Combine the logs (product rule): log₂(x(x − 2)) = 3.
- Rewrite in exponential form: x(x − 2) = 2³ = 8.
- Rearrange and factor: x² − 2x − 8 = 0, so (x − 4)(x + 2) = 0 and x = 4 or x = −2.
- Check the domain: log₂(−2) is undefined, so x = −2 is rejected. The only solution is x = 4 (log₂4 + log₂2 = 2 + 1 = 3).
That last line is the one answer-only tools and rushed students skip. A good step-by-step solution always shows it.
Solve your equation, with the working
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The algebra mistakes that cost the most marks
Most lost marks in algebra come from a handful of repeat errors, not from not knowing the topic. Here is what to watch for.
| Mistake | Wrong | Right |
|---|---|---|
| Not distributing a negative | 5 − (2x − 3) = 5 − 2x − 3 | 5 − (2x − 3) = 8 − 2x |
| Dividing by a variable that can be zero | x² = 3x, divide by x: x = 3 | x² − 3x = 0, x(x − 3) = 0: x = 0 or x = 3 |
| Not flipping an inequality | −2x < 6 gives x < −3 | −2x < 6 gives x > −3 |
| Keeping an extraneous root | √(x + 2) = x gives x = 2 or x = −1 | Only x = 2 works; √1 = 1, not −1 |
| Sign slip when moving a term | 3x − 14 = 5x + 6 becomes −2x = 6 − 14 | −2x = 6 + 14 = 20 |
Two of these deserve a closer look. Dividing by a variable silently deletes a solution, because you can't divide by x if x might be zero. Factor instead. Extraneous roots appear whenever you square both sides or use logs: squaring √(x + 2) = x gives x² − x − 2 = 0, which has roots 2 and −1, but only 2 satisfies the original equation. The fix for both is the same habit: substitute every answer back into the original equation.
How to read a step-by-step solution (so it actually helps)
- Attempt the problem first. Even a half-finished attempt tells you exactly where you got stuck, which is the line to study.
- Name the rule on each line. For every step, say what was done: "distributed," "subtracted 5x from both sides," "applied the product rule for logs." If you can't name it, that's your gap.
- Find the first line where you and the solution differ. Everything after an early mistake is usually fine method on wrong numbers.
- Cover it up and redo it. Close the solution and solve the same problem from a blank page. Then do a similar problem with different numbers.
- Check the last line. Substitute the answer back in. If the solution you are reading doesn't include a check, do one yourself.
What algebra can it solve?
- Linear equations and inequalities: one variable or systems.
- Quadratics: factoring, completing the square, the quadratic formula.
- Functions: composition and evaluation, e.g. finding f(−2 − g(3)) given f(x) and g(x).
- Exponents and logarithms: solving, simplifying, change of base.
- Matrices and linear systems: determinants, inverses, augmented matrices, and "for what values of a and b…" consistency questions.
- Word problems: the AI sets up the equation from the sentences first, then solves it.
- Beyond algebra: derivatives, integrals and limits are covered in our calculus solver with steps guide.
Stuck on the same step every time?
Scan a few problems from the same topic and compare the solutions. The repeated first move (isolate the variable, factor first, take the log of both sides) is the pattern your teacher wants you to internalize. Your History tab keeps them side by side, tagged by subject and searchable. When you think you've got it, verify your own answers on the next problem set instead of scanning first.