+2446
First, let me show you a wrong approach. I almost fell for it myself:
\(\frac{1}{\frac{6}{2}}=\frac{1}{6}*\frac{1}{2}=\frac{1}{12}\)
This math above is simple, but this would imply that the probability of rolling a 6 is 1/12. Well, you'll see...
If you combine the probabilities of all events occurring, then the probability should be 1. Let's try that with our current answer. Let's test it:
| \(\frac{1}{12}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=1\) | Create a common denominator, first |
| \(\frac{1}{12}+\frac{2}{12}+\frac{2}{12}+\frac{2}{12}+\frac{2}{12}+\frac{2}{12}=1\) | Add the numerators |
| \(\frac{11}{12}=1\) | This is a false statement |
11/12 is not equal to one 1. Therefore, the probability cannot of rolling a 6 cannot be 1/12. However, there's a trick that we can use. How can we make 11/12=1? That's right, multiply by its reciprocal, 12/11. Therefore, multiply all of your fractions by it:
\(\frac{12}{11}(\frac{1}{12}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6})\)
But wait! WE only need the probability of rolling a 6, so we only need to multiply 12/11 by 1/12!
\(\frac{12}{11}*\frac{1}{12}=\frac{12}{132}=\frac{1}{11}\)
As you'll see below, there are other methods to do this problem. Of course, the method above is what I chose. Isn't it beautiful how multiple approaches still leads to the same final answer?
.+2446 \(x=6\hspace{1cm}x=26\)
Here is the original equation:
\(x\pm10=16\)
What is this telling us? This equation is really 2 separate equations. I've laid them out for you:
Now do you understand what \(\pm\) means? It means that you both add and subtract. Solve each equation separately, and you get both values for x. I'll start with the first:
| \(x+10=16\) | Subtract 10 on both sides to isolate x |
| \(x=6\) | |
Of course, you aren't done yet! You must solve the other equation, too:
| \(x-10=16\) | Add 10 on both sides to isolate x |
| \(x=26\) | |
Therefore, you have 2 solutions:
\(x=6\) and \(x=26\)
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