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How do you solve algebraic equations with only 1 variable that appears multiple times?

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For clarity you should avoid using this division symbol and use spacing/parentheses to make sure everyone understands what you mean. Do you mean x/8 + x = 54 as written or x/(8+x) = 54?
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The key thing is: no matter what you do, you have to maintain the equals sign. The equals sign means that both sides are the same value, and this is something you have to preserve. You can think of the equation as a balanced scale, and no matter what you do, you have to maintain balance.

So if you add/subtract/multiply/divide something on the left, you have to add/subtract/multiply/divide the same thing on the right.

To solve for a variable, you want to add/subtract/multiply/divide (or any other mathematical operation) in such a way that it leaves only the variable on one side of the equation and everything else on the other.

x÷8+x=54

The first thing I would do in this case is get rid of the 8. You're dividing by an 8, so to get rid of it, you would multiply by 8 since a dividing a number by itself cancels it out leaving just a 1. And, remember, whatever we do to one side we have to do to the other, so we have to multiply both sides by 8:

8(x÷8+x)=8(54)

8\*x÷8 + 8x = 432

x + 8x = 432

Now, we can combine our x's:

9x = 432

All we have left is the 9. Since we're multiplying by it, we now divide by 9 on both sides:

9x/9 = 432/9

x = 48

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