alleryStart learning →Classify the equation 10 + 4(p - 5) = 0, then state the solution.
AIt is an identity; the solution is all real numbers
BIt is conditional; the solution is p = 5/2
CIt is a contradiction; there is no solution
DIt is conditional; the solution is p = -5/2
Answer & Solution
Correct answer: B. It is conditional; the solution is p = 5/2
1. Distribute on the left: 10 + 4(p - 5) becomes 10 + 4p - 20, which simplifies to 4p - 10.
2. The equation is now 4p - 10 = 0, so 4p = 10 after adding 10 to both sides.
3. Divide both sides by 4 to get p equals five-halves.
4. Since the equation is true only for this one value of p, it is a conditional equation with solution p = 5/2.
_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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