AI Algebra Solver

What the AI algebra solver can do

Type an equation such as 3(x + 2) = 2x + 11 and the solver expands the brackets, gathers like terms, moves the unknown to one side and checks the result by substitution. It also handles single expressions: simplify, expand or evaluate them when there is no equals sign.

• Solve for x in linear equations with brackets, fractions and unknowns on both sides.
• Simplify expressions by collecting like terms and applying the distributive law.
• Expand products such as (x + 3)(x − 2).
• Rearrange formulas to make a chosen letter the subject, for example solving 2x + 3y = 12 for y.

How algebra rules are applied, in order

Every algebra solution follows the same logic: whatever you do to one side of an equation you must do to the other. The solver works in a fixed order so the working is easy to follow.

1. Clear brackets and fractions using the distributive law or a common multiplier.
2. Collect like terms on each side, so each side has at most one x-term and one number.
3. Move unknowns to one side by adding or subtracting the same term from both sides.
4. Undo the remaining operations in reverse order of BIDMAS: add or subtract first, then multiply or divide.
5. Check by putting the answer back into the original equation.

When to use algebra tools instead of a calculator

A calculator evaluates numbers; algebra works with letters that stand for numbers you do not know yet. If your question contains a variable, you need a method rather than a button press. Use this page when you want the method, and the more specialised pages when the topic is narrower: the linear equation solver for first-degree equations, the quadratic equation solver for x², and the factoring calculator for breaking expressions into brackets.

Worked examples

Example 1: Solve 3(x + 2) = 2x + 11

1. Expand the bracket: 3x + 6 = 2x + 11.
2. Subtract 2x from both sides: x + 6 = 11.
3. Subtract 6 from both sides: x = 5.
4. Check: 3(5 + 2) = 21 and 2(5) + 11 = 21 ✓

Final answer: x = 5

Example 2: Simplify 2(3x − 4) − 5(x − 2)

1. Expand the first bracket: 6x − 8.
2. Expand the second bracket, watching the sign: −5x + 10.
3. Combine like terms: 6x − 5x = x and −8 + 10 = 2.

Final answer: x + 2

Example 3: Expand (x + 3)(x − 2)

1. Multiply each term in the first bracket by each term in the second: x·x, x·(−2), 3·x, 3·(−2).
2. This gives x² − 2x + 3x − 6.
3. Collect the x-terms: −2x + 3x = x.

Final answer: x² + x − 6

Example 4: Make y the subject of 2x + 3y = 12

1. Subtract 2x from both sides: 3y = 12 − 2x.
2. Divide every term by 3: y = 4 − (2/3)x.

Final answer: y = 4 − 2x/3

Common mistakes to avoid

• Forgetting to multiply every term inside a bracket: 3(x + 2) is 3x + 6, not 3x + 2.
• Dropping a negative sign when expanding a bracket that has a minus in front of it.
• Doing an operation to one side only, which changes the equation.
• Combining unlike terms: 2x and 3x² cannot be added into 5x³.
• Skipping the final check, which catches most arithmetic slips in seconds.

Frequently asked questions

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