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I am very confused;

If I needed to solve this equation

$$12 = 3x$$

Isn't the answer $x = 0.25$? Why does the calculator state that it is $x = 4$? (Symbolab)

Does the answer change based on if it's $12 = 3x$ or $3x = 12$? Does the side matter? Or can we divide with any number?

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  • $\begingroup$ Divide both sides of the equation by 3. Then $x=12/3=4$. The side doesnt matter. $\endgroup$ – Wuestenfux Feb 12 at 12:18
  • $\begingroup$ Because to have the equation in the form $\;x={}$, you have to divide both sides by $3$. $\endgroup$ – Bernard Feb 12 at 12:22
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    $\begingroup$ Try always to add, subtract, multiply or divide both sides of an equation by a number. Don't, don't, don't MOVE numbers. Ignore your teacher if they tell you to "move the 3 to the other side". $\endgroup$ – Paul Feb 12 at 12:23
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    $\begingroup$ "What number am I? You'll get twelve if you triple me." $\endgroup$ – Michael Hoppe Feb 12 at 14:20
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    $\begingroup$ Please explain why you think that $x=0.25$ (and not $x=4$) is the correct answer. $\endgroup$ – Martin R Feb 12 at 14:37
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Check your answer then you will see $3\cdot 0.25=0.75$ and this is clearly not $4$.

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If three packages of eggs has a dozen eggs, how many eggs does one package have? e.g. $3x = 12 \implies x = ?$

Hint:

enter image description here

It's easiest to think of $12$ partitioned into three groups. Alternatively, it's trivial to partition $3x$ into three groups [e.g. each group is of size $x$]. But, because $3x$ and $12$ are equal to to one another, each of their 3-partitions are equal as well [e.g. $3x=12\implies 3x = 3\cdot 4 \implies x=4$]. Of course it's just as easy to divide both sides by three.

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$$12 = 3x$$ $$\to\frac 13 (12)=\frac 13 (3x)$$ $$\to \frac{12}{3}=x$$ $$\to 4=x$$

Calculator is right, and the order of the sides doesn't matter.

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I don't know how you managed to get $0.25$, but the reason your calculator says that it's $4$ is because that actually is the right answer.

An equation generally means what you have on one side of the equation is equal (that's what the equals sign does) to that which you have on the other side of the equation. In other words, the number on the left should be exactly the same as the number on the right. This means that $12$ is the same number as $3x$. This in turn means that dividing $12$ by $3$ numerically should be equivalent to dividing $3x$ by $3$. Dividing $12$ by $3$ gives you $4$ and dividing $3x$ by $3$ gives you $x$. So, the result that you get is:

$$ 4=x $$

The order in which you read an equation does not matter. It's the same thing either way you look at. So, the result above states that $x=4$. And that's your final answer.

You can check your work by replacing $x$ with $4$:

$$ 12=3\cdot4\\ 12=12 $$

As you can see both sides contain the same number, as it should be.

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  • $\begingroup$ The 0.25 comes from moving the 3 to the other side I should think. Then the 12 drops down (and why not, if things move?) and you have 3/12. It could just as easily have been 9 or -12/3 too. $\endgroup$ – Paul Feb 12 at 13:57

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