Help with solving 1/10(x+8) - 1/15(x-5) = 1 for x

Here is the problem

1/10(x+8) - 1/15(x-5) = 1

How would you solve this and what would x equal?

I would solve it by algebraic manipulation and x woul dequal the value that makes the equality true.

First, please clarify meaning by adding parentheses.

Do you mean \(\displaystyle \frac{1}{10*(x+8)}\) or \(\displaystyle \frac{1}{10}*(x+8)\)?

If you mean the former, try (1/10)*(x+8). If you mean the latter, you have it right, but 1/[10*(x+8)] is less confusing.

I mean the latter, just for clarification.

I still can't figure out what x equals.

\(\displaystyle \L \frac{x+8}{10} + \frac{x-5}{15} = 1\)

common denominator is 30 ...

\(\displaystyle \L \frac{3(x+8)}{30} + \frac{2(x-5)}{30} = \frac{30}{30}\)

multiplying every term by 30 yields the equation ...

\(\displaystyle \L 3(x+8) + 2(x-5) = 30\)

can you work it out from this point?

Why do you have x + 8/10 + x-5/15, when it's 1/10*x+8 - 1/15*x-5?

Anyway, the answer is x = -4, correct?

You're missing the point.

What does 1/10*x+8 mean?

This: \(\displaystyle \frac{1}{10}*(x+8)\)

This: \(\displaystyle \frac{1}{10*x}+8\)

This: \(\displaystyle \frac{1}{10*x+8}\)

This: \(\displaystyle (\frac{1}{10}*x)+8\)

Unfortunately, by convention, the last one is what you have written.

Note: \(\displaystyle \frac{1}{10}*(x+8)\,=\frac{x+8}{10}\)

So, really, just what is the question? We can keep guessing, but you've seen already that it is not very productive.

I meant the last one. But, skeeter already helped me find the answer. -4 is correct, right?

kaze950 said:

I meant the last one. But, skeeter already helped me find the answer. -4 is correct, right?

Click to expand...

YES; but using 3(x + 8) - 2(x - 5) = 30

By "last one", you really mean the first one, or the one mentioned in the note, I guess. I'm so confused. See how important it is to write clearly?

Ya; plus you're NOT listening:

"Why do you have x + 8/10 + x - 5/15......"

You were told to be CLEAR; then you come back with above:
x + 8/10 should be (x + 8) / 10, similarly (x - 5) / 15 : there's a BIG difference :shock:

Okay, the reason I asked that question is why he was adding the fractions when in the problem, they are being subtracted.

I don't know how clearer I can get though.

(1/10)(x+8) - (1/15)(x-5) = 1

which becomes

(x+8/10) - (x-5/15)

which becomes

(12/30) - (-18/30) = 30/30

or

(12/30) + (18/30) = 30/30

So, x = -4

kaze950 said:

(1/10)(x+8) - (1/15)(x-5)

which becomes

(x+8/10) - (x-5/15)

Click to expand...

You're not getting it. This step you have written is incorrect.

x+8/10 = x+(8/10) = x+(4/5) = (5x+4)/5
x-5/15 = x-(5/15) = x-(1/3) = (3x-1)/3

I suspect that is NOT what you intended.

Written carefully, one gets

(1/10)(x+8) - (1/15)(x-5) = 1

Multiply by 5, just for practice

(1/2)(x+8) - (1/3)(x-5) = 5

Multiply by 3

(3/2)(x+8) - (x-5) = 15

Multiply by 2

(3)(x+8) - (2)(x-5) = 30 (Of course, would could have multiplied by 30 in the first place.)

Expand, using the Distributive Property

3x + 24 - 2x + 10 = 30

Rearrange (Commutative Property)

3x - 2x + 24 + 10 = 30

Combine Like Term (Associative Property)

(3x - 2x) + (24 + 10) = 30
x + 34 = 30

Subtract 34

x = 30 - 34 = -4

There are NO holes in that notation. Every step says what it is supposed to mean. Careful, clear, consistent, comprehensible. No slopiness. You will pay a price for that, later.

Quick TK: go edit

...and it's REALLY irritating to get sloppy right at the end!