So this is a rational equation. So to find the value of x you must do the act of cancelling or isolating.
The equation is like this am I right?
[tex]8 \times \frac{x}{12} = \frac{x}{13} - 9[/tex]
In the left side of the equation, times sign or no times sign, it is still the same.
[tex]8 \times \frac{x}{12} = 8 \frac{x}{12} [/tex]
Lets continue on to the equation:
First lets focus on the left side:
Turn the number 8 into a fraction, that would be 8/1.
[tex] \frac{8}{1} \times \frac{x}{12} = \frac{x}{13} - 9[/tex]
Then, we need to factor the numbers:
What are the factors of 8?
8=2*2*2*2
What about factors of 1?
1=1
What about the factors of 12?
2*2*3
Factors of x?
x=x
Now let us cancel the same factors on the numerators to the factors of the denominators:
[tex] \frac{2 \times 2 \times 2}{1} \times \frac{x}{2 \times 2 \times 3} [/tex]
Cancel the two 2 pairs:
[tex] \frac{2}{1} \times \frac{x}{3} [/tex]
Now multiply the numerators and denominators:
[tex] \frac{2 \times x}{1 \times 3} = \frac{2x}{3} [/tex]
Now we are done solving for the left side, now its turn for us to solve for the right side:
Again, make the whole number (9) into a fraction, that would be 9/1
[tex] \frac{x}{13} - \frac{9}{1} [/tex]
Now its time for us to subtract these fractions:
(For me, the butterfly shortcut method is easier)
So the answer would be:
[tex] \frac{x}{13} - \frac{9}{1} = \frac{x - 117}{13} [/tex]
Now we are done with the both sides of the equation. This is the result:
[tex] \frac{2x}{3} = \frac{x - 117}{13} [/tex]
But we're not done yet
Now we need to cross-multiply (the easiest method for me) meaning we need to multiply the numerator on the left side to the denominator on the right side and vice versa.
[tex]2x \times 13 = 3 \times (x - 117)[/tex]
[tex]26x = 3x - 351[/tex]
We're getting really close, one step and we are done! (End my typing suffering, PLEASEEE!!!)
Now its isolating time!
Here is a fill-in-the-blanks question:
3x-__=0
The answer would be 3x right? (Because 3x-3x=0)
Wait I accidentally pressed save please be patient for the answer
Ill just say the answer for you: the answer is: x=-351/23 (yes its a fraction)
