Study tips · 3 min read
How to Check Your Math Answers: Five Reliable Methods
1. Inverse operations
Undo the calculation. If 1,236 ÷ 3 = 412, then 412 × 3 should return 1,236: 1236.
2. Substitution
Put your answer back into the original equation.
Substitution check is built into the solver
Step-by-step working 4 steps
- 1Write the equation
3x + 5 = 2x − 7
- 2Collect the x terms on the left
3x − 2x = −7 − 5 x = −12
Subtract the smaller x term and the constant from both sides, so x is alone on the left and numbers are on the right.
- 3Divide by the coefficient of x
x = −12 ÷ 1 = −12
- 4Check by substituting back
Left: 3(−12) + 5 = −31 Right: 2(−12) − 7 = −31
Both sides match, so the solution is correct.
3. Estimation
Round first and see if the answer is the right size — see estimation techniques.
4. A second method
Solve a different way. A quadratic can be factored and also solved with the formula: x = 3 or x = 2.
x² − 5x + 6 = 0 by formula
- Factored form: (x − 3)(x − 2)
- Discriminant D = 1
- Vertex: (2.5, −0.25)
Step-by-step working 6 steps
- 1Identify a, b and c
x² − 5x + 6 = 0 a = 1, b = −5, c = 6
- 2Calculate the discriminant
D = b² − 4ac = (−5)² − 4(1)(6) = 1
D is positive: two different real roots.
- 3Apply the quadratic formula
x = (−b ± √D) / 2a = (5 ± √1) / 2 = (5 ± 1) / 2
- 4Solve for both roots
x₁ = 3 x₂ = 2
- 5Check by substitution
f(3) = 0 f(2) = 0
Both should be 0 (allowing for tiny rounding).
- 6Vertex of the parabola
x = −b / 2a = 2.5, y = −0.25 → vertex (2.5, −0.25)
The parabola opens upward, so the vertex is the minimum point.
5. Units and sense
Do the units match the question, and is the size sensible? A person 17 m tall or a 250% discount signals an error. Use the scientific calculator steps to find where a slip happened.
Frequently asked questions
Is a calculator enough to check?
It confirms arithmetic but not that you set the problem up correctly; use substitution and estimation too.
What if my two methods disagree?
Recheck each step; the disagreement shows an error in at least one.
Keep reading
10 Common Algebra Mistakes (With Numbers That Prove They’re Wrong)
The ten algebra errors students make most often, each disproved with a quick numerical check — (a+b)² ≠ a²+b², √(a+b) ≠ √a+√b, and more.
Study tipsEstimation Techniques: Get Close Fast and Catch Mistakes
Round to leading digits, use benchmark fractions and compensate to estimate sums, products and percentages — with exact answers to show how close you get.
ConceptsThe Quadratic Formula: Where It Comes From
A short derivation of the quadratic formula by completing the square, the meaning of the discriminant, and a worked example you can check with the solver.
Charts & referencesAlgebra Formulas Cheat Sheet: Identities, Exponents, Quadratics
The algebra formulas you need most: special products, exponent and log rules, the quadratic formula, slope and distance, with a worked check.