How to get better at algebra
You get better at algebra by finding the one or two steps that keep breaking and practising those, not by doing more of everything. Most algebra mistakes come from a short list: negative signs, distributing, fractions, exponents and factoring. Find which one is yours, fix it, and every topic built on it gets easier.
The five problems below show you which step it is. They take about three minutes.
The plan was right: multiply both sides by 6 to clear the fractions. But only the fractions got multiplied. The 2 and the −1 were left as they were. See the fix.
Why more practice doesn't work on its own
The usual advice is to do more problems. That works only if the problems are aimed at the right thing.
Think about what a page of algebra homework is made of. Each problem has one new idea in it and four or five lines of older skills around it. If one of those older skills is unreliable, you can do thirty problems and get most of them wrong for the same reason every time, without ever seeing what the reason is.
So the order matters. First find the step, then practise it, then build the habit that catches it when it slips again.
Step 1: find the step that breaks
Almost every algebra mistake is one of five kinds. Try each problem below before you open the answer, on paper or with igni checking your steps. Each answer also shows the most common wrong result, so you can see whether that slip is yours.
1. Negative signs
A minus sign in front of a bracket changes every sign inside it. This is the most common slip in all of algebra.
Simplify 5 − (2x − 3)
Solve it with igni igni checks each step as you go. It won't give you the answer.
Show the answer
5 − 2x + 3 = 8 − 2x.
If you got 2 − 2x, the minus sign reached the 2x but not the −3. Signs are your step.
2. Distributing
Multiplying a bracket means multiplying every term in it, including when the bracket is squared.
Expand (x + 3)2
Solve it with igni igni checks each step as you go. It won't give you the answer.
Show the answer
(x + 3)(x + 3) = x2 + 6x + 9.
If you got x2 + 9, you squared each term separately and lost the middle term. Distributing is your step.
3. Fractions
Fractions with letters follow the same rules as fractions with numbers. If the number version was never solid, the letter version won't be.
Simplify x/2 + x/3
Solve it with igni igni checks each step as you go. It won't give you the answer.
Show the answer
3x/6 + 2x/6 = 5x/6.
If you got 2x/5, you added the tops and the bottoms. Fractions are your step.
4. Exponents
There are only a few exponent rules, but they look alike, and mixing up two of them gives an answer that looks reasonable.
Simplify (2x3)2
Solve it with igni igni checks each step as you go. It won't give you the answer.
Show the answer
22 × x3×2 = 4x6.
If you got 2x6, the power didn't reach the 2. If you got 4x5, you added the exponents when they should be multiplied. Either way, exponents are your step.
5. Factoring
Factoring is distributing in reverse. It is the step that most often stops a longer problem halfway.
Factor x2 − 16
Solve it with igni igni checks each step as you go. It won't give you the answer.
Show the answer
(x − 4)(x + 4).
If you got (x − 4)2, or decided it can't be factored, factoring is your step.
How to read your result.
One or two wrong or slow: you have found your target. Go to step 2 with just those.
Three or more: start with negative signs and fractions. The other three depend on them.
All five right: your basics are fine, and the slips are happening inside longer problems. Step 3 is the one for you.
Step 2: practise that one step
Now that you know the step, give it its own practice. A few rules make that practice count.
Keep it narrow
If signs are the problem, do problems that are only about signs. Fifteen to twenty of exactly that kind teach more than a mixed worksheet where the skill shows up twice.
Spread it out
Ten minutes a day for a week works better than one long session. The point is to make the step automatic, and that comes from coming back to it.
Start from a blank page
Reading a worked solution feels like learning, because every line makes sense as you read it. Writing the solution yourself is a different skill. We wrote more about why watching isn't enough.
Then mix it back in
After a few days, go back to your normal homework and watch for that step inside bigger problems. That is where it has to hold.
Step 3: check every line with a number
Algebra has a built-in way to check your work that most students never use. Two expressions that are equal must give the same result when you put the same number in for x. So after you rewrite a line, pick a number and try both versions.
Is 5 − (2x − 3) the same as 2 − 2x? Try x = 2.
The first line is the original. The second is the wrong version, and it gives a different number. The third is the right one. The check takes ten seconds.
Two tips. Don't check with 0 or 1, because they hide mistakes: (x + 3)2 and x2 + 9 both give 9 when x = 0. And when you solve an equation, put your answer back into the original equation, not into your own second line.
This is the algebra version of the habit we describe in how to get better at math: check at the step, not at the answer.
The check on a full problem
Here is the problem from the top of the page: solve x/3 + 2 = x/2 − 1. A student writes this:
Put x = 3 back into the original. The left side is 3/3 + 2 = 3. The right side is 3/2 − 1 = 1/2. They don't match, so something broke.
The mistake is on line 2. Multiplying both sides by 6 means multiplying every term by 6, and the 2 and the −1 were skipped. Here it is with that line fixed:
Check: 18/3 + 2 = 8 and 18/2 − 1 = 8. Both sides match.
The student didn't need to learn equations again. They needed one rule, and a check that told them which line to look at.
Algebra 1, Algebra 2, and how long this takes
How do you get better at Algebra 1?
In Algebra 1, the gaps usually come from before algebra: negative numbers and fractions. Fix those two first, then practise solving equations until checking your answer in the original equation is a habit.
If Algebra 1 is your first course with letters in it, give yourself some time. Everyone finds the switch from numbers to letters strange at first.
How do you get better at Algebra 2?
In Algebra 2, the gaps usually come from Algebra 1: factoring, exponent rules and distributing. Most students also arrive after a year of Geometry, so part of the problem is rust. Redo Algebra 1 problems for the first two weeks alongside your homework.
We go through the course in more detail in is Algebra 2 hard? — and the course after it assumes all of this too, which is most of what makes precalculus hard.
How long does it take to get better at algebra?
One specific gap, like negative signs or fractions, can often be closed in two to three weeks of short, focused practice. Speed and confidence across a whole course take longer, usually a term.
If you have a test this week, pick the single step that costs you the most points and work only on that.
Why am I bad at algebra when I was fine at math before?
Usually because algebra is where shortcuts from arithmetic stop working. With numbers you can often see the answer. With letters you have to follow the rules exactly, so small habits like dropping a sign start to cost you. That is a fixable habit, not a lack of ability.
If one bad grade has turned into dreading the subject, read about math anxiety and how confidence gets built.
A check on every line, without stopping to do it yourself
Step 3 works, but it is slow to do by hand on every line, and it is easy to skip when you are tired. That is the part igni does.
Solve your homework the way you normally would — on paper, snapping each step as you go, or typed straight into igni. After each line, igni tells you whether it still matches the line before.
You still do the algebra
igni never gives you the answer. You do the work; igni shows you which line broke.
It follows your method
A correct route your teacher didn't show still gets confirmed rather than marked wrong.
Step 1, without the quiz
When the flagged lines keep being the same kind of step, you've found your step without taking a test for it.
Flagged on line two, before the wrong answer gets written. Multiplying by 6 was the right idea; it has to reach every term.