The first step is to identify the order in which the equation must be solved, by following PEMDAS (you might know it as BEDMAS):
Parenthesis (or Brackets)
Exponents
Multiplication and Division
Addition and Subtraction
My advice would be to add parenthesis, following these rules, if you are not very good at finding them immediately by sight.
So:
![4 - 5 / 2 * (\frac{1}{10x}) = 1\\\\4 - [(5/2)*(\frac{1}{10x})]=1\\\\4-(2.5*\frac{1}{10x})=1\\\\4-\frac{2.5}{10x}-1=0\\3-\frac{x}{4}=0\\\frac{x}{4}=3\\x=3*4\\x=12](https://tex.z-dn.net/?f=4%20-%205%20%2F%202%20%2A%20%28%5Cfrac%7B1%7D%7B10x%7D%29%20%20%3D%201%5C%5C%5C%5C4%20-%20%5B%285%2F2%29%2A%28%5Cfrac%7B1%7D%7B10x%7D%29%5D%3D1%5C%5C%5C%5C4-%282.5%2A%5Cfrac%7B1%7D%7B10x%7D%29%3D1%5C%5C%5C%5C4-%5Cfrac%7B2.5%7D%7B10x%7D-1%3D0%5C%5C3-%5Cfrac%7Bx%7D%7B4%7D%3D0%5C%5C%5Cfrac%7Bx%7D%7B4%7D%3D3%5C%5Cx%3D3%2A4%5C%5Cx%3D12)
We check our answer:
![x=12\\4 - [(5 / 2) * (1/10)*(x)] = 1\\4 - [(5 / 2) * (\frac{1}{10}) * (12))] = 1\\4 - [2.5 * (\frac{1}{10})*12] = 1\\4 - [(\frac{2.5}{10})*12] = 1\\4 - [(\frac{1}{4})*12] = 1\\4 - 3 = 1\\1=1](https://tex.z-dn.net/?f=x%3D12%5C%5C4%20-%20%5B%285%20%2F%202%29%20%2A%20%281%2F10%29%2A%28x%29%5D%20%3D%201%5C%5C4%20-%20%5B%285%20%2F%202%29%20%2A%20%28%5Cfrac%7B1%7D%7B10%7D%29%20%2A%20%2812%29%29%5D%20%3D%201%5C%5C4%20-%20%5B2.5%20%2A%20%28%5Cfrac%7B1%7D%7B10%7D%29%2A12%5D%20%3D%201%5C%5C4%20-%20%5B%28%5Cfrac%7B2.5%7D%7B10%7D%29%2A12%5D%20%3D%201%5C%5C4%20-%20%5B%28%5Cfrac%7B1%7D%7B4%7D%29%2A12%5D%20%3D%201%5C%5C4%20-%203%20%3D%201%5C%5C1%3D1)
We are right!
So, 
.
1 and 4 will be the expression that makes the equatio. true for all values of x to prove i have done it in the picture attached in this message
Answer:
Use the Quadratic formula
Answer:
1. 
2. 
3. 
4. ![40^{\frac{2}{3}}=4\sqrt[3]{25} =4325](https://tex.z-dn.net/?f=40%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%3D4%5Csqrt%5B3%5D%7B25%7D%20%3D4325)
5. Step 4: 
6. 
Step-by-step explanation:
Use the following properties:
![a^{\frac{x}{y} } =\sqrt[x]{a^{y} }](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7Bx%7D%7By%7D%20%7D%20%3D%5Csqrt%5Bx%5D%7Ba%5E%7By%7D%20%7D)
![\sqrt[n]{ab} =\sqrt[n]{a} \sqrt[n]{b}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bab%7D%20%3D%5Csqrt%5Bn%5D%7Ba%7D%20%5Csqrt%5Bn%5D%7Bb%7D)
So:
1. ![27^{\frac{2}{3} } =\sqrt[3]{27^{2}} =\sqrt[3]{729} }=9](https://tex.z-dn.net/?f=27%5E%7B%5Cfrac%7B2%7D%7B3%7D%20%7D%20%3D%5Csqrt%5B3%5D%7B27%5E%7B2%7D%7D%20%3D%5Csqrt%5B3%5D%7B729%7D%20%7D%3D9)
2. 
3. ![(-243)^{\frac{3}{5} } =\sqrt[5]{-243^{3} } =\sqrt[5]{-14348907} =-27](https://tex.z-dn.net/?f=%28-243%29%5E%7B%5Cfrac%7B3%7D%7B5%7D%20%7D%20%3D%5Csqrt%5B5%5D%7B-243%5E%7B3%7D%20%7D%20%3D%5Csqrt%5B5%5D%7B-14348907%7D%20%3D-27)
4. ![40^{\frac{2}{3}}=\sqrt[3]{40^{2} } =\sqrt[3]{2^{6} 5^{2} } =\sqrt[3]{2^{6} } \sqrt[3]{5^{2} } =2^{\frac{6}{3} } 5^{\frac{2}{3} } =4 *5^{\frac{2}{3} } =4\sqrt[3]{5^{2} } =4\sqrt[3]{25}=4325](https://tex.z-dn.net/?f=40%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%3D%5Csqrt%5B3%5D%7B40%5E%7B2%7D%20%7D%20%3D%5Csqrt%5B3%5D%7B2%5E%7B6%7D%205%5E%7B2%7D%20%7D%20%3D%5Csqrt%5B3%5D%7B2%5E%7B6%7D%20%7D%20%5Csqrt%5B3%5D%7B5%5E%7B2%7D%20%7D%20%3D2%5E%7B%5Cfrac%7B6%7D%7B3%7D%20%7D%205%5E%7B%5Cfrac%7B2%7D%7B3%7D%20%7D%20%3D4%20%2A5%5E%7B%5Cfrac%7B2%7D%7B3%7D%20%7D%20%3D4%5Csqrt%5B3%5D%7B5%5E%7B2%7D%20%7D%20%3D4%5Csqrt%5B3%5D%7B25%7D%3D4325)
5. 
6.
![(-8c^{9} d^{-3} )^{\frac{1}{3} } *(6c^{-1}d^{4})^{2} =\sqrt[3]{-8} c^{3} d^{-1} 36c^{-2} d^{8} \\\\-2c^{3} d^{-1} 36c^{-2} d^{8}=-72cd^{7}](https://tex.z-dn.net/?f=%28-8c%5E%7B9%7D%20d%5E%7B-3%7D%20%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%20%7D%20%2A%286c%5E%7B-1%7Dd%5E%7B4%7D%29%5E%7B2%7D%20%3D%5Csqrt%5B3%5D%7B-8%7D%20c%5E%7B3%7D%20d%5E%7B-1%7D%2036c%5E%7B-2%7D%20d%5E%7B8%7D%20%5C%5C%5C%5C-2c%5E%7B3%7D%20d%5E%7B-1%7D%2036c%5E%7B-2%7D%20d%5E%7B8%7D%3D-72cd%5E%7B7%7D)
If we find the unit rate for the graph, that means it's proportional. For the first question, we could see that the unit rate is 2/1, so it's proportional.
