Difference between revisions of "1967 AHSME Problems/Problem 7"
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== Solution == | == Solution == | ||
| − | <math>\ | + | Notice that <math>b</math> and <math>d</math> are irrelevant to the problem. Also notice that the negative sign is irrelevant since <math>c</math> can be any real number. So the question is equivalent to asking what values <math>a</math> can take on given the inequality <math>a<c</math>. The answer, is of course, that <math>a</math> could be anything, or <math>\boxed{\textbf{(E) } \ a \; \text{can be positive, negative, or zero}}</math> |
| + | |||
| + | ~ proloto | ||
== See also == | == See also == | ||
| − | {{AHSME box|year=1967|num-b=6|num-a=8}} | + | {{AHSME 40p box|year=1967|num-b=6|num-a=8}} |
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 18:41, 28 September 2023
Problem
If 
where 
, 
, 
, and 
are real numbers and 
, then:
Solution
Notice that and are irrelevant to the problem. Also notice that the negative sign is irrelevant since can be any real number. So the question is equivalent to asking what values can take on given the inequality 
. The answer, is of course, that could be anything, or 
~ proloto
See also
| 1967 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
