the equilibrium point, is when Demand = Supply, namely, when the amount of "Q"uantity demanded by customers is the same as the Quantity supplied by vendors.
That occurs when both of these equations are equal to each other.
let's do away with the denominators, by multiplying both sides by the LCD of all fractions, in this case, 12.
![\bf \stackrel{\textit{Supply}}{-\cfrac{3}{4}Q+35}~~=~~\stackrel{\textit{Demand}}{\cfrac{2}{3}Q+1}\implies \stackrel{\textit{multiplying by 12}}{12\left( -\cfrac{3}{4}Q+35 \right)=12\left( \cfrac{2}{3}Q+1 \right)} \\\\\\ -9Q+420=8Q+12\implies 408=17Q\implies \cfrac{408}{17}=Q\implies \boxed{24=Q} \\\\\\ \stackrel{\textit{using the found Q in the Demand equation}}{P=\cfrac{2}{3}(24)+1}\implies P=16+1\implies \boxed{P=17} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{Equilibrium}{(24,17)}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7BSupply%7D%7D%7B-%5Ccfrac%7B3%7D%7B4%7DQ%2B35%7D~~%3D~~%5Cstackrel%7B%5Ctextit%7BDemand%7D%7D%7B%5Ccfrac%7B2%7D%7B3%7DQ%2B1%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20by%2012%7D%7D%7B12%5Cleft%28%20-%5Ccfrac%7B3%7D%7B4%7DQ%2B35%20%5Cright%29%3D12%5Cleft%28%20%5Ccfrac%7B2%7D%7B3%7DQ%2B1%20%5Cright%29%7D%20%5C%5C%5C%5C%5C%5C%20-9Q%2B420%3D8Q%2B12%5Cimplies%20408%3D17Q%5Cimplies%20%5Ccfrac%7B408%7D%7B17%7D%3DQ%5Cimplies%20%5Cboxed%7B24%3DQ%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Busing%20the%20found%20Q%20in%20the%20Demand%20equation%7D%7D%7BP%3D%5Ccfrac%7B2%7D%7B3%7D%2824%29%2B1%7D%5Cimplies%20P%3D16%2B1%5Cimplies%20%5Cboxed%7BP%3D17%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20%5Cstackrel%7BEquilibrium%7D%7B%2824%2C17%29%7D~%5Chfill)
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percent.
![\bf A = \{ x~|~x \in \mathbb{N}; x\leq 3 \}](https://tex.z-dn.net/?f=%5Cbf%20A%20%3D%20%5C%7B%20x~%7C~x%20%5Cin%20%5Cmathbb%7BN%7D%3B%20x%5Cleq%203%20%5C%7D)
![\bf x\leq 3\implies x\in \{0,1,2,3\}\implies \green{\boxed{\bf A = \{0,1,2,3\}}}](https://tex.z-dn.net/?f=%5Cbf%20%20x%5Cleq%203%5Cimplies%20x%5Cin%20%5C%7B0%2C1%2C2%2C3%5C%7D%5Cimplies%20%5Cgreen%7B%5Cboxed%7B%5Cbf%20A%20%3D%20%5C%7B0%2C1%2C2%2C3%5C%7D%7D%7D)
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![\bf B = \{ x~|~x \in \mathbb{N};~ 9\leq x^{2}\leq 36 \}](https://tex.z-dn.net/?f=%5Cbf%20B%20%3D%20%5C%7B%20x~%7C~x%20%5Cin%20%5Cmathbb%7BN%7D%3B~%209%5Cleq%20x%5E%7B2%7D%5Cleq%2036%20%5C%7D)
![\bf 9\leq x^{2}\leq 36\Rightarrow 3^{2} \leq x^{2}\leq 6^{2}\Rightarrow 3\leq x\leq 6\Rightarrow x\in\{3,4,5,6\}](https://tex.z-dn.net/?f=%5Cbf%209%5Cleq%20x%5E%7B2%7D%5Cleq%2036%5CRightarrow%203%5E%7B2%7D%20%5Cleq%20x%5E%7B2%7D%5Cleq%206%5E%7B2%7D%5CRightarrow%203%5Cleq%20x%5Cleq%206%5CRightarrow%20x%5Cin%5C%7B3%2C4%2C5%2C6%5C%7D)
![\bf x\in \{3,4,5,6\}\implies \blue{\boxed{\bf B = \{3,4,5,6\}}}](https://tex.z-dn.net/?f=%5Cbf%20%20%20x%5Cin%20%5C%7B3%2C4%2C5%2C6%5C%7D%5Cimplies%20%5Cblue%7B%5Cboxed%7B%5Cbf%20B%20%3D%20%5C%7B3%2C4%2C5%2C6%5C%7D%7D%7D)
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![\bf C = \{ x~|~x \in \mathbb{N};~ 3< x\leq 7\}](https://tex.z-dn.net/?f=%5Cbf%20C%20%3D%20%5C%7B%20x~%7C~x%20%5Cin%20%5Cmathbb%7BN%7D%3B~%203%3C%20x%5Cleq%207%5C%7D)
![\bf 3](https://tex.z-dn.net/?f=%5Cbf%203%3Cx%5Cleq%207%5CRightarrow%20x%5Cin%5C%7B4%2C5%2C6%2C7%5C%7D%5CRightarrow%5Cpurple%7B%5Cboxed%7B%5Cbf%20C%20%3D%20%5C%7B4%2C5%2C6%2C7%5C%7D%7D%7D)
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![\bf D = \{ x~|~x \in \mathbb{N};~ 8\leq x^{3}\leq 100 \}](https://tex.z-dn.net/?f=%5Cbf%20D%20%3D%20%5C%7B%20x~%7C~x%20%5Cin%20%5Cmathbb%7BN%7D%3B~%208%5Cleq%20x%5E%7B3%7D%5Cleq%20100%20%5C%7D)
![\bf 8\leq x^{3}\leq 100\Rightarrow 2^{3} \leq x^{3}\leq 4^{3}\Rightarrow 2\leq x\leq 4\Rightarrow x\in\{2,3,4\}](https://tex.z-dn.net/?f=%5Cbf%208%5Cleq%20x%5E%7B3%7D%5Cleq%20100%5CRightarrow%202%5E%7B3%7D%20%5Cleq%20x%5E%7B3%7D%5Cleq%204%5E%7B3%7D%5CRightarrow%202%5Cleq%20x%5Cleq%204%5CRightarrow%20x%5Cin%5C%7B2%2C3%2C4%5C%7D)
![\bf x\in \{2,3,4\}\implies \red{\boxed{\bf D = \{2,3,4\}}}](https://tex.z-dn.net/?f=%5Cbf%20%20%20x%5Cin%20%5C%7B2%2C3%2C4%5C%7D%5Cimplies%20%5Cred%7B%5Cboxed%7B%5Cbf%20D%20%3D%20%5C%7B2%2C3%2C4%5C%7D%7D%7D)
![==Salmon==](https://tex.z-dn.net/?f=%3D%3DSalmon%3D%3D)
The answer is undoubtedly 6,4
Answer:
-6+4p
Step-by-step explanation:
-(6-4p)
-1(6-4p)
-1*6=-6
-1*-4p=4p
-6+4p