Difference between revisions of "2005 AMC 12A Problems/Problem 2"
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| + | {{Duplicate|[[2005 AMC 12A Problems|2005 AMC 12A #2]] and [[2005 AMC 10A Problems|2005 AMC 10A #3]]}} | ||
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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. 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 \Longrightarrow x = -2, \quad -2b - 10 = -2 \Longrightarrow -2b = 8 \Longrightarrow b = | + | <math>2x + 7 = 3 \Longrightarrow x = -2, \quad -2b - 10 = -2 \Longrightarrow -2b = 8 \Longrightarrow b = \boxed{\textbf{(B)}-4}</math> |
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| + | ==Video Solution== | ||
| + | CHECK OUT Video Solution: https://youtu.be/GmOEQzJVAn4 | ||
| + | |||
| + | ==Video Solution 2== | ||
| + | https://youtu.be/c_Zxp8iwCD4 | ||
| + | ~Charles3829 | ||
== See also == | == See also == | ||
{{AMC12 box|year=2005|num-b=1|num-a=3|ab=A}} | {{AMC12 box|year=2005|num-b=1|num-a=3|ab=A}} | ||
| − | + | {{AMC10 box|year=2005|ab=A|num-b=2|num-a=4}} | |
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 18:06, 25 December 2022
- 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
Video Solution
CHECK OUT Video Solution: https://youtu.be/GmOEQzJVAn4
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
