I need help with the break down of this problem. I need to know exactly what I need to do to solve this problem. Please help!
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4$\begingroup$ Can you solve for $y$ in $-6+y=-5$? Then multiply what you got by $4$, and you're done. $\endgroup$– Pedro ♦Commented Apr 18, 2013 at 20:32
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2 Answers
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Hint: What do you have to add to $-6$ to get $-5$? What do you have to divide by $4$ to get the answer to my previous question?
answered Apr 18, 2013 at 20:32
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$\begingroup$ Put another way: $$-6+\frac x4=-5\\-6+\frac x4=-6+1\\\frac x4=1\\\frac x4=\frac44\\x=4$$ $\endgroup$ Commented Apr 18, 2013 at 21:13
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$\begingroup$ and the solution of $$\sin(x)=\sin(\varphi)$$ is $x=\varphi$ ? $\endgroup$ Commented Sep 26, 2013 at 21:20
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$\begingroup$ @miracle173: That is a solution, certainly. The difference there is that we're no longer dealing with only one-to-one functions. $\endgroup$ Commented Sep 27, 2013 at 6:00
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$\begingroup$ That is what I wanted to point to.When I read your description and your example it looks like pattern matching. But pattern matching is not sufficient to find all solution as the example $\sin(x)=\sin(\varphi)$ shows. The essential steps (subtracting $-6$ from and mutliplying $4$ to both side of the equation) are not mentioned. I think representing $-5$ as $-6 +1$ and $1$ as $\frac{4}{4}$ is absolutely dispensable and guides in the wrong direction. $\endgroup$ Commented Sep 27, 2013 at 9:20
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$\begingroup$ @miracle173: For linear equations, pattern matching is equivalent to the standard ("two-step") approach that any textbook provides (and Bob provides below). Since the user didn't know what to do, I gathered that the standard approach wasn't intuitive, so I provided an alternative. Had it seemed that the user was anywhere near the level of trigonometric or other many-to-one functions, I might have advised caution for this approach, but it didn't, so I didn't. $\endgroup$ Commented Sep 27, 2013 at 14:42
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I would think it through this way:
The first task is to get the x term (x times something) by itself on one side, and everything else on the other side of the equation. You can do that by adding 6 to both sides (to cancel the -6). Then you have:
$$\frac{x}{4} = 1$$
Now you want to get x all by itself, so you can multiply both sides by 4:
$$x = 4$$
Done.
