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The question is $x-7=28$ But I'm not sure if when I subtract do I have to change the signs to negative?

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    $\begingroup$ Judging by your other questions, this problem should be a piece of cake for you. :) $\endgroup$ – Lays Apr 22 '13 at 22:26
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    $\begingroup$ @GustavoBandeira I have seen some friends of mine trying to teach children using this same methodology: picturing the "=" sign as a bridge which numbers change their signs when they pass through it. I think this is a disservice to mathematical thinking. $\endgroup$ – Marra Apr 22 '13 at 22:31
  • $\begingroup$ @GustavoBandeira too many Gustavos! But thanks, I didn't know that. $\endgroup$ – Lays Apr 22 '13 at 22:42
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    $\begingroup$ I really can't believe this question has received so much attention. $\endgroup$ – dezign Apr 22 '13 at 23:09
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If you have to solve it for $x$, then what you have is that $x-7$ and $28$ are the same numbers, that is $$ x-7=28 $$ Therefore, if you add 7 to this number, then both expressions for it remain equal, that is $$ (x-7)+7=28+7 $$ But that is the same as $$ x+(-7+7)=35 $$ therefore $$ x=35 $$ which is the answer.

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$x-7=28$

$x-7+7=28+7$

$x=35$


You always do the same operation on both side. You can add something or substract something (witch is the same things as adding the opposite) but you always do the same thing on both sides.

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The idea with solving equations is that it has to mean the same thing it did before if you do the same thing to both sides.

What can you do to make $x-7$ simpler? You add seven to it. That gives you $x-7+7=x$ on the left-hand side.

Since we have to do the same thing to both sides, you have to add seven to the other side as well. You get $28+7=35$ over there.

This gives you the equation

$$x = 35$$

which is probably what you wanted!

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Subtraction is the same as adding the opposite (adding the same number with the sign changed). So, you could subtract $-7$ from both sides, which is the same as adding $7$ to both sides.

You might instead think of $x-7=28$ as saying that $28$ is $7$ less than $x$, which means that $x$ is $7$ more than $28$, so $x$ is $35$. Or, write it in a chain of equalities starting with $x$ and making $x-7$ show up: $$\begin{align}x &= x+0\\ &= x+(-7+7)\\ &= (x+-7)+7\\ &= (x-7)+7\\ &= 28+7\qquad\qquad (\text{substitute }28\text{ for }x-7\text{, since they're equal})\\ &= 35.\end{align}$$

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Lol, I hope I remember this correctly!

Whenever, there's a = between numbers and one number is shifted from one side to the other, the sign ALWAYS changes.

As per your equation x - 7 = 28

No sign means a + sign so the equation can be written as (+)x (-)7 = (+)28

To know the value of x simply take -7 to the opposite side. -7 will change into +7. Hence,

x = 28 + 7 = 35

Examples

x + 2 = 1
x = 1 - 2 (Since 2 is the bigger number b/w 1 & 2, the final answer will take it's sign)
x = - 1

-x - 2 = 1
-x = 1 + 2
-x = 3 ( to make x positive shift it to the right and bring 3 to the left)
-3 = x

-x -2 = -1
-x = -1 + 2
-x = 1
-1 = x

-x + 2 = -1
-x = -1 -2 ( - and - = + , since 2 is the bigger number, the final answer has a - sign)
-x = -3
3 = x

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You add $7$ to each side, getting $x=35$

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