alleryStart learning →Solve for n: (2/5)n = 14.
An = 35
Bn = 28
Cn = 70
Dn = 5.6
Answer & Solution
Correct answer: A. n = 35
1. The coefficient of n is the fraction 2/5, so multiply both sides by its reciprocal, 5/2.
2. On the left, (5/2)(2/5)n = n, since reciprocals multiply to 1.
3. On the right, (5/2)(14) = 70/2 = 35, so n = 35.
4. Check: (2/5)(35) = 70/5 = 14, a true statement.
5. n = 5.6 is the trap of multiplying 14 by 2/5 instead of by the reciprocal 5/2.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations and Inequalities", section 2.2 Solve Equations using the Division and Multiplication Properties of Equality_
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