-2x/x+6+5=-x/x+6

Question

I really can not figure out this math problem, help

Answer 1

This question is slightly hard to read due to a lack of parentheses, but I believe the question is:

-2x   +   5  =  -x

x+6               x+6

 

The easiest way to solve this is to add x/(x+6) to both sides, leaving:

-x  + 5      =    0

x+6

 

Then subtract 5 from each side of the equation, and multiply each side by x+6:

 

-x = -5(x+6)

 

Multiplying each side by -1 (to make it simpler) and distributing the 5 leaves you with:

 

x = 5x + 30

 

Subtract 5x from each side to arrive at:

 

-4x = 30

 

Finally, divide each side of the equation by -4 to arrive at your answer:

 

x = -7.5

 

 

You can check this answer by plugging x back into the original equation, like so:

 

-2(-7.5)  +  5  = -(-7.5)

(-7.5)+6           (-7.5)+6

 

(15/-1.5) + 5 = (7.5/-1.5)

-10 + 5 = -5

-5 = -5

Answer 2

This problem is called a rational equation because the Xs are in the deminators of the fractions. To solve a rational equation, you have to find the common denominator, just like you do when you add or subtract normal fractions. Here, the common denominator is X+6 because two of the fractions have that denominator, and the third one, the 5, has a denominator of 1, which can go into anything. Once you have figured out what the common denominator is, multiply each term by the common denominator. So, in this case, you would multiply 2x/(x+6), 5, and -x/(x+6) each by (x+6). In the first term and the last term the (x+6) would cancel out on the top and bottom to leave you what was orginally in the numerator, -2x and -x. In the case of the 5, you need to distribute it to the (x+6) to get 5x+30. Your equation should now look like this: -2x +5x+30 = -x. You can then simplify and solve this like a normal linear equation. First, combine like terms on the left to get 3x + 30 =-x. Then, subtract 3x from both sides to get 30 = -4x. Finally, divide both sides by -4 to get x = -15/2. You can always check your asnwer by substituting it in for x in the original to see if you get the same number on both sides of the equal sign. 

Answer 3

Nadia,.

You should simplify the rational expression by multiplying both sides of the equation by x +6.  This will eliminate x + 6 out of the denominator and you have a simple algebraic expression.  You would have:  -2x + 5(x + 6) = -x.  Now simply distribute the 5, combine like terms, and solve for x.  You will find x to be -7.5.

 

This should help.  Let me know

Deron

Answer 4

-2x/x + 6 + 5 = -x/x +6

-2 +6 +5 = -1 +6

9 = 5 is a contradiction proving there is no real solution

UNLESS you ignore PEMDAS order of operations

then

-2x/(x+6)+ 5 = -x/(x+6)

x/(x+6) = 5 cross multiply

5x +30 = x

4x =-30

x=-30/4 = - 7.5

that's the answer you likely want

BUT it could also be

-2x/(x+6+5) = -x(x+6)

-x/(x+11) = -x(x+6)

1/(x+11) = 1/(x+6)

x+11 = x+6

11=6 is another contradiction proving no real solution

although there are two surreal solutions

x = infinity and negative infinity

infinty + a finite real number = infinity

one of the paradoxes of the math of infinity

pioneered by mathematician Cantor who literally went insane thinking about infinity. So don't think about it too much or you may enter the twilight zone or your brain will.

Answer 5

-2x/x+6+5=-x/x+6

REWRITE EQUATION, ADDING A DENOMINATOR TO THE 2ND TERM

-2x / (x+6) + 5 / 1 = -x / (x+6)

Multiply each fraction by (x+6), the common denominator.

1st step:

(x+6) /1 times (-2x) / (x+6) = -2x because the (x+6) crosses out

2nd step:

(x+6) /1 times 5 / 1 = 5 (x+6) by multiplying the numerators

3rd step:

(x+6) /1 times -x / (x+6) = -x because (x+6) crosses out

REWRITE EQUATION WITH THE NEW VALUES

-2x + 5 (x+6) = -x

THEN SOLVE FOR X -- FOLLOW STEPS, AS SUMMARIZED BELOW

-2x + 5x + 30 = -x multiply 5 (x+6)

3x + 30 = -x add -2x + 5x

4x + 30 = 0 add x to both sides

4x = -30 subtract 30 from both sides

4x / 4 = -30 / 4 divide by 4

x = -15/2

x = -7 1/2 OR -7.5

NOTE: x + 6 can never equal 0 because the denominator cannot equal 0

SOLVE FOR X

x + 6 = 0

x +6 -6 = 0 -6

x = -6

X CANNOT EQUAL -6 BECAUSE x + 6 = -6 +6 = 0

Answer 6

Dear Nadia,

The first thing I am going to do in this situation is multiply each SIDE of the equals sign by the common denominator of (x + 6).  That way, that miserable denominator of (X + 6) will be obliterated on both sides and that is a relief.  However, this must be done correctly as each side must be multiplied by that common denominator and the left side of the equals sign CONTAINS TWO TERMS.  To make a long story short, both the fraction and the number 5 must be multiplied by (X + 6) in the first step.

It becomes:    -2x + 5(X + 6) = -x

Which simplifies (when you distribute) to:  -2x + 5x + 30 = -x

Combine like terms to simplify:  3x + 30 = -x

If we add X to each side and subtract 30 FROM EACH SIDE we get the following:

4x = -30  And then we divide each side by 4 to get the answer:  X = -7.5

Best Wishes, Mr. Gets Results

 

Answer 7

has no solution