1. mathstudent55

Is the 6 part of the denominator? It's hard to understand what you mean the way you wrote it.

2. mathstudent55

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

i dont know thats the way it is written

4. anonymous

@ mathstudent55 yes that is the way the question looks exactly

5. mathstudent55

Oh, great. Then you wrote it correctly.

6. mathstudent55

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

I got -1/7 would that be correct

8. mathstudent55

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

Yes now i minus 6 from both sides which gives me -1/7x=12 After that is where im stuck

10. anonymous

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

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

ok cook i got x=-84

13. mathstudent55

@Ivanskodje You did a great job solving that equation and showing and explaining each step, but unfortunately, you solved the wrong equation.

14. mathstudent55

x = -84 is correct.

15. anonymous

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

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

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

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

Ah, I understand - VERY useful information! Thank you :) (Sorry again for the hijack)

20. JohnN.

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