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1) Determine if the following statement is true or false. If false, provide a counterexample:

"An equation with an integer coefficient will always have an integer solution.".

2) Write a rel-world problem that could be solved by using the equation 3x - 25 = 125

3) Solve (x + 5)(x + 5) = 49. (Hint: There are two solutions)

Spirit In Motion
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  • The first two are answered well below. For the third, try "foiling" them together to get $$\left(x+5\right)\left(x+5\right)=x^2+10x+25,$$ and set this equal to 0 by subtracting the 49 from the right side to the left to get $$ x^2+10x-24=0, $$ which implies that $x=12$ or $x=-2$, because 12 and -2 add up to 10 and can be multiplied to get -24. There are two solutions because the degree of the polynomial tells us there are two; for a polynomial of the third degree, a cubic function, we should have three roots, and so on. – bjd2385 Nov 18 '14 at 22:41
  • Thanks a lot! I am very grateful! :) – Spirit In Motion Nov 18 '14 at 23:29

1 Answers1

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1) not true, $3x=25\implies x=\frac{25}{3}$

2)We want to calculate how many coats we have to sell at 3 dollars a piece to get 125 dollars profit, given that there is an overhead cost of 25 dollars. I'm 3)$(x+5)^2=49\implies x+5=7$ or $x+5=7\implies x=12$ or $x=2$

Community
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NickC
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