Difference between revisions of "1959 AHSME Problems/Problem 25"
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<math>\textbf{(A)}\ x^2<49 \qquad\textbf{(B)}\ x^2>1 \qquad\textbf{(C)}\ 1<x^2<49\qquad\textbf{(D)}\ -1<x<7\qquad\textbf{(E)}\ -7<x<1</math> | <math>\textbf{(A)}\ x^2<49 \qquad\textbf{(B)}\ x^2>1 \qquad\textbf{(C)}\ 1<x^2<49\qquad\textbf{(D)}\ -1<x<7\qquad\textbf{(E)}\ -7<x<1</math> | ||
== Solution == | == Solution == | ||
| − | The equation <math>|3-x| < 4</math> can be solved by splitting it into two inequalities: <math>3-x<4</math> and <math>3-x<-4</math>. The solutions to those inequalities are <math>x<-1</math> and <math>x>7</math>, respectively. The common interval of those two inequalities is <math>\textbf{(D)}\ -1<x<7</math> | + | The equation <math>|3-x| < 4</math> can be solved by splitting it into two inequalities: <math>3-x<4</math> and <math>3-x<-4</math>. The solutions to those inequalities are <math>x<-1</math> and <math>x>7</math>, respectively. The common interval of those two inequalities is <math>\boxed{\textbf{(D)}\ -1<x<7}</math>. |
== See also == | == See also == | ||
{{AHSME 50p box|year=1959|num-b=24|num-a=26}} | {{AHSME 50p box|year=1959|num-b=24|num-a=26}} | ||
{{MAA Notice} | {{MAA Notice} | ||
Revision as of 12:25, 21 July 2024
Problem 25
The symbol 
means 
if 
is greater than or equal to zero, and 
if a is less than or equal to zero; the symbol 
means "less than";
the symbol 
means "greater than."
The set of values 
satisfying the inequality 
consists of all such that:
Solution
The equation 
can be solved by splitting it into two inequalities: 
and 
. The solutions to those inequalities are 
and 
, respectively. The common interval of those two inequalities is 
.
See also
| 1959 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 24 |
Followed by Problem 26 | |
| 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 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
{{MAA Notice}
