Verify a solution

High School

Definition

The process to prove the solution is true and correct. Often asked in a variable equation question, it requires the substitution of one or more variables to verify the equations or inequalities of the problem. For example: verify that x=2 is the solution of the equation X + 3 = 5.

Worked examples

\(x + 3 = 5\) when \(x = 2\): substitute to get \(2 + 3 = 5\), which simplifies to \(5 = 5\) ✓

Since both sides equal 5, the equation is true and \(x = 2\) is verified as the correct solution.

\(3y - 7 = 2\) when \(y = 3\): substitute to get \(3(3) - 7 = 9 - 7 = 2\), so \(2 = 2\) ✓

Follow order of operations when substituting, then check if both sides are equal.

Common mistakes

Substituting \(x = 2\) into \(x + 3 = 5\) gives \(2 + 3 = 2\) → \(2 + 3 = 5\), then compare to the right side: \(5 = 5\) Substitute into the left side expression, then check if it equals the right side—don't replace both sides with the solution.
\(2x = 6\) when \(x = 3\): \(2(3) = 2\times 3\), verified ✓ → \(2(3) = 6\), so \(6 = 6\) ✓ You must complete the arithmetic and confirm both sides have the same numerical value.
If \(4 \ne 4\) after substituting, the solution is still correct → If both sides are unequal, the proposed solution is wrong Verification fails when the two sides don't match—that means the value is not a solution.

Where you'll use it next

You'll verify solutions throughout algebra when solving linear and quadratic equations, systems of equations, and later when checking roots of polynomial and rational equations in precalculus.

Found in 1 StudyPug lesson

Mastering the Art of Determining Solutions in Linear Equations

Grade 10 Math

Unlock the power of linear equations! Learn to confidently determine the number of solutions in various scenarios, from single equations to complex systems. Enhance your problem-solving skills today.

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