algebra: 3x=18 Explanation: What I did is I got the highest number that both numbers divide to.
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Well, the very first thing I'd note is that you've replaced one equation of the form (something)x = (something else) with a different equation of the same form. That's not particularly helpful; all your work was basically for nothing in that case. That aside, the next thing I'd note is that if you're ever unsure of an answer, you can always check it yourself. Here, we can immediately show that the answer cannot possibly be correct by plugging in a test value of \(x\).
Suppose \(x = 1\). Then your answer states we should have \(2(1) = 3\), but that's obviously false. What if \(x = 2\)? Then we'd have \(2(2) = 3\), again an obviously false result. However, the actual values output are 2 and 4 respectively, so to me that suggest maybe we should try a middle point? Suppose \(x = 1.5\). This would yield \(2(1.5) = 3\) which is true. However, we encounter a wrinkle. In order for your answer to be correct, both your new equation and the old equation have to be true for the same value(s) of \(x\). If we plug in \(x = 1.5\) into the original equation we get another obviously false statement: \(6(1.5) = 18\).
Now that we've figured out your answer is incorrect, it's only natural to ask why it's incorrect. What went wrong? You say you "got the highest number that both numbers divide [in]to" and this was, supposedly, 6. But how did you come by this number? How did you decide that \(3x\) is cleanly divisible by 6? If we assume \(x = 1\), we see that 3(1) = 3 is not divisible by 6. Nor is it the case if \(x = 3\), as 3(3) = 9 is not divisible by 6 either.
It may help you to really truly think about what it means to have a variable in a problem. The expression \(3x\) means exactly the same as \(3 \cdot (\text{some number})\). Writing it in this way ought to make it crystal clear that the expression \(3x\) is definitely divisible by 3. And it should be equally clear that 18 is also divisible by 3.
Recalling that division "undoes" multiplication, what do you get when you divide the expression \(3x\) by 3? What do you get when you divide 18 by 3? What does it mean that these two new quantities are equal?
Suppose \(x = 1\). Then your answer states we should have \(2(1) = 3\), but that's obviously false. What if \(x = 2\)? Then we'd have \(2(2) = 3\), again an obviously false result. However, the actual values output are 2 and 4 respectively, so to me that suggest maybe we should try a middle point? Suppose \(x = 1.5\). This would yield \(2(1.5) = 3\) which is true. However, we encounter a wrinkle. In order for your answer to be correct, both your new equation and the old equation have to be true for the same value(s) of \(x\). If we plug in \(x = 1.5\) into the original equation we get another obviously false statement: \(6(1.5) = 18\).
Now that we've figured out your answer is incorrect, it's only natural to ask why it's incorrect. What went wrong? You say you "got the highest number that both numbers divide [in]to" and this was, supposedly, 6. But how did you come by this number? How did you decide that \(3x\) is cleanly divisible by 6? If we assume \(x = 1\), we see that 3(1) = 3 is not divisible by 6. Nor is it the case if \(x = 3\), as 3(3) = 9 is not divisible by 6 either.
It may help you to really truly think about what it means to have a variable in a problem. The expression \(3x\) means exactly the same as \(3 \cdot (\text{some number})\). Writing it in this way ought to make it crystal clear that the expression \(3x\) is definitely divisible by 3. And it should be equally clear that 18 is also divisible by 3.
Recalling that division "undoes" multiplication, what do you get when you divide the expression \(3x\) by 3? What do you get when you divide 18 by 3? What does it mean that these two new quantities are equal?
Steven G
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You divided 6 by 3 and got 2, ok. You divided 6 by 18 and got 3. Nope! 6/18 = 1/3. It is 18/6 = 3. In any case you should divide both sides by 3 or.......It's all about how you read it. You read it correctly and you know your times tables these problems have no level of difficulty. I read 3x=6 as three times what number is 6. Since I know that 3*2=6 I conclude that x=2
If I am given x+5 =7 I ask myself what number plus five equals seven. Since I know that 2 + 5 =7, then I know that x=2