2005 AMC 12A Problems/Problem 2: Difference between revisions
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== Problem == | == Problem == | ||
The equations <math>2x + 7 = 3</math> and <math>bx - 10 = - 2</math> have the same solution. What is the value of <math>b</math>? | The equations <math>2x + 7 = 3</math> and <math>bx - 10 = -2</math> have the same solution <math>x</math>. What is the value of <math>b</math>? | ||
<math> | <math> | ||
\textbf{(A) } -8 \qquad \textbf{(B) } -4 \qquad \textbf{(C) } -2 \qquad \textbf{(D) } 4 \qquad \textbf{(E) } 8 | |||
</math> | </math> | ||
== Solution == | == Solution == | ||
<math>2x + 7 = 3 \ | <math>2x + 7 = 3 \iff x = -2</math>, so we require <math>-2b-10 = -2 \iff -2b = 8 \iff b = \boxed{\textbf{(B) } -4}</math>. | ||
==Video Solution 1== | |||
https://youtu.be/GmOEQzJVAn4 | |||
==Video Solution 2== | |||
https://youtu.be/c_Zxp8iwCD4 | |||
~Charles3829 | |||
== See also == | == See also == | ||
Latest revision as of 16:01, 1 July 2025
- The following problem is from both the 2005 AMC 12A #2 and 2005 AMC 10A #3, so both problems redirect to this page.
Problem
The equations 
and 
have the same solution 
. What is the value of 
?
Solution
, so we require 
.
Video Solution 1
Video Solution 2
~Charles3829
See also
| 2005 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 1 |
Followed by Problem 3 |
| 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 | |
| All AMC 12 Problems and Solutions | |
| 2005 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 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 | ||
| All AMC 10 Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America. 
