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Solving an equation removes the variable and leaves the statement 14 equals 14. What does that show?
AIt is a contradiction, no solution
BIt has exactly one solution value
CIt has exactly two solution values
DIt is an identity, all reals work
Answer & Solution
Correct answer: D. It is an identity, all reals work
1. The variable terms cancelled, so the variable never mattered.
2. What is left, 14 equals 14, is true no matter what was substituted.
3. An equation true for every value of the variable is an identity.
4. Its solution is all real numbers, so a single solution value is ruled out.
_Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.1 Use a General Strategy to Solve Linear Equations_
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