+2441 Order of operations is a strict set of rules that dictate how to evaluate any expression. I have laid the order of operations out for you:
1. Simplify within grouping symbols such as parentheses or brackets from left to right.
2. Simplify exponents from left to right.
3. Perform multiplication or division, whichever operation comes first from left to right.
4. Perform addition or subtraction, whichever operation comes first from left to right.
If something is higher on the list, then it has greater priority. Let's apply this knowledge to this particular problem:
| \(-17+(\textcolor{red}{18-14})-(-14)\) | First, do what is in parentheses first, as that is given the highest priority. |
| \(-17+4\textcolor{red}{-(-14)}\) | -(-14) is an example of multiplication, which is now the highest priority. |
| \(\textcolor{red}{-17+4}+14\) | It is time to perform addition. Since there are two instances of addition, the order of operations states that we must perform that from left to right. |
| \(\textcolor{red}{-13+14}\) | This is the only simplification that is left to do. |
| \(1\) | |
+2441 All that is necessary is some simplifying. That's all.
| \(2(3-\sqrt{3})-3(1-\sqrt{3})=a+b\sqrt{3}\) | Let's simplify the left-hand side as much as possible and see if there is any parallelism. The first step is to distribute. |
| \(6-2\sqrt{3}-3+3\sqrt{3}=a+b\sqrt{3}\) | Now, combine like terms together. |
| \(\)\(\textcolor{red}{3}+\textcolor{blue}{1}\sqrt{3}=\textcolor{red}{a}+\textcolor{blue}{b}\sqrt{3}\) | I have used colors to highlight the parallelism between the left-hand side and the right-hand side. This means that I have written the original expression in the desired form, \(a+b\sqrt{3}\) |
+2441 Hey guest,
Let's try and solve for the question mark. Note that I have replaced the question mark with a more standard symbol, x. Below is a representation of the equation in LaTeX form:
\(1\frac{3}{5}(1999*\frac{1}{24}+x)-3\frac{5}{11}*3\frac{2}{3}=127\)
| \(1\frac{3}{5}(1999*\frac{1}{24}+x)-3\frac{5}{11}*3\frac{2}{3}=127\) | Mixed numbers may be nice to look at, but they are fairly clumsy when algebraic computation is involved. I will convert all mixed numbers into improper fractions. |
| \(\frac{8}{5}(\frac{1999}{24}+x)-\frac{38}{11}*\frac{11}{3}=127\) | Let's do some simplification and distribution. |
| \(\frac{8}{5}*\frac{1999}{24}=\frac{1}{5}*\frac{1999}{3}=\textcolor{red}{\frac{1999}{15}}\\ \frac{38}{11}*\frac{11}{3}=38*\frac{1}{3}=\textcolor{blue}{\frac{38}{3}}\) | |
| \(\textcolor{red}{\frac{1999}{15}}+\frac{8}{5}x-\textcolor{blue}{\frac{38}{3}}=127\) | In general, I recommend for situations like this to multiply both sides by the LCD. This will eliminate all instances of fractions. The LCD, in this case, is 15. |
| \(1999+24x-190=1905\) | Let's do some more simplification on the left-hand side of the equation. |
| \(24x+1809=1905\) | Subtract 1809 on both sides. |
| \(24x=96\) | Divide by 24 on both sides to isolate x completely. |
| \(x=4\) | |
