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anonymous

  • one year ago

please help solve x -2/7x+6+1/7x=18

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  1. mathstudent55
    • one year ago
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    Is the 6 part of the denominator? It's hard to understand what you mean the way you wrote it.

  2. mathstudent55
    • one year ago
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    You wrote: \(-\dfrac{2}{7} x + 6 + \dfrac{1}{7} x = 18\) but I have a feeling this is not what you meant.

  3. anonymous
    • one year ago
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    i dont know thats the way it is written

  4. anonymous
    • one year ago
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    @ mathstudent55 yes that is the way the question looks exactly

  5. mathstudent55
    • one year ago
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    Oh, great. Then you wrote it correctly.

  6. mathstudent55
    • one year ago
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    First, add the two fractions on the left side of the equal sign. Since they are like terms (both have x), and they have the same denominator, the addition of the two fractions is straight forward.

  7. anonymous
    • one year ago
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    I got -1/7 would that be correct

  8. mathstudent55
    • one year ago
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    What is \(-\dfrac{2}{7} x + \dfrac{1}{7} x\) ? You are correct with the addition of fractions, since -2/7 + 1/7 = -1/7, but remember there is x in both, so the sum is \(-\dfrac{1}{7} x\) Now we have \(-\dfrac{1}{7} x + 6 = 18\) Ok so far?

  9. anonymous
    • one year ago
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    Yes now i minus 6 from both sides which gives me -1/7x=12 After that is where im stuck

  10. anonymous
    • one year ago
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    It is important that you understand how to "move around" the math. It can be done by multiplying, dividing, adding or subtracting sides or joints (joints are separated by + and -) Start: \[-\frac{ 2 }{ 7x } + 6 + \frac{ 1 }{ 7x } = 18\] Multiply every joint with 7x; \[-2 + (7x*6) + 1 = (7x*18)\] Add together where you can; \[-1 + 42x = 126x\] Put X on one side (done by subtracting both sides with -42x); \[126x - 42x = -1\] Add together; \[84x = -1\] Divide both sides with 84, turning 84x/84 to only x; \[x = -\frac{ 1 }{ 84 }\]

  11. mathstudent55
    • one year ago
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    Correct. Now since x is being multiplied by -1/7, you need to multiply both sides by the reciprocal of -1/7. The reciprocal of a number is simply flipping the number (if it is written as a fraction.) \(-\dfrac{1}{7} x = 12\) \(- 7 \cdot (-\dfrac{1}{7}) x = -7 \cdot 12\)

  12. anonymous
    • one year ago
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    ok cook i got x=-84

  13. mathstudent55
    • one year ago
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    @Ivanskodje You did a great job solving that equation and showing and explaining each step, but unfortunately, you solved the wrong equation.

  14. mathstudent55
    • one year ago
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    x = -84 is correct.

  15. anonymous
    • one year ago
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    I read -2/7x+6+1/7x=18 as -2/(7x) (...) - Sorry for hijacking, but is the division a higher priority than the multiplication in this case? (Always learning) :)

  16. mathstudent55
    • one year ago
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    Strictly speaking, -2/7x should be read as (-2)/(7) * x, so x is not in the denominator. In this case, the poster actually wrote the problem correctly, but many times people don't use parentheses where they should, and you can't tell what they mean.

  17. mathstudent55
    • one year ago
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    As far as order of operations is concerned, here is an important point. Let's say you use PEMDAS as your guide. It is important to understand how PEMDAS is used. Most people don't understand it. People think that the order is exactly the order that the initials stand for, but it is not so. PEMDAS is more accurately written as: P E MD AS which means, first do (P)arentheses. Then do (E)xponents Now come (MD) then do multiplications and divisions in the order they appear from left to right. Finally, do (AS) additions and subtractions in the order they appear from left to right.

  18. mathstudent55
    • one year ago
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    Your observation above is excellent. It is not just here that a division is done before a multiplication. Notice from PEMDAS above that multiplications and divisions are the same level of operation and are done in the order they appear from left to right. If a division appears before a multiplication it is always done before the multiplication. The same applies to additions and subtractions. These two operations are on the same level of priority, so they are done in the order they appear from left to right. Additions do not have priority over subtractions as a general rule.

  19. anonymous
    • one year ago
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    Ah, I understand - VERY useful information! Thank you :) (Sorry again for the hijack)

  20. JohnN.
    • one year ago
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    Let's solve your equation step-by-step. −27x+6+17x=18 Step 1: Simplify both sides of the equation. −27x+6+17x=18 Simplify: (Show steps) −17x+6=18 Step 2: Subtract 6 from both sides. −17x+6−6=18−6 −17x=12 Step 3: Multiply both sides by 7/(-1). (7−1)*(−17x)=(7−1)*(12) x=−84 Answer: x=−84

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