alleryStart learning →Classify the equation 6(2n - 1) + 3 = 2n - 8 + 5(2n + 1), then state the solution.
AIt is an identity; the solution is all real numbers
BIt is a contradiction; there is no solution
CIt is conditional; the solution is n = 0
DIt is conditional; the solution is n = 1
Answer & Solution
Correct answer: A. It is an identity; the solution is all real numbers
1. Distribute and combine on the left: 6(2n - 1) + 3 becomes 12n - 6 + 3, which simplifies to 12n - 3.
2. Distribute and combine on the right: 2n - 8 + 5(2n + 1) becomes 2n - 8 + 10n + 5, which simplifies to 12n - 3.
3. Subtracting 12n from both sides leaves -3 = -3, which is always true.
4. Since both sides are always equal, the equation is an identity, and its solution is all real numbers.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations and Inequalities", section 2.4 Use a General Strategy to Solve Linear Equations_
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