Answer:
A iS THE ANSWER
Step-by-step explanation:
Answer:
![x=2](https://tex.z-dn.net/?f=x%3D2)
Step-by-step explanation:
When given the following equation;
![\frac{x+3}{3x-2}-\frac{x-3}{3x+2}=\frac{44}{9x^2-4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B3%7D%7B3x-2%7D-%5Cfrac%7Bx-3%7D%7B3x%2B2%7D%3D%5Cfrac%7B44%7D%7B9x%5E2-4%7D)
One has to solve for the variable (x). Remember, when working with fractions, one must have a common denominator in order to perform operations. Since the denominators on the left side of the equation are unlike, one must change them so that they are like denominators. Multiply each fraction by the other fraction's denominator on the respective side. Remember to multiply both the numerator and denominator by the value to ensure that the equation remains true.
![=\frac{x+3}{3x-2}*(\frac{3x+2}{3x+2})-\frac{x-3}{3x+2}*(\frac{3x-2}{3x-2})=\frac{44}{9x^2-4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%2B3%7D%7B3x-2%7D%2A%28%5Cfrac%7B3x%2B2%7D%7B3x%2B2%7D%29-%5Cfrac%7Bx-3%7D%7B3x%2B2%7D%2A%28%5Cfrac%7B3x-2%7D%7B3x-2%7D%29%3D%5Cfrac%7B44%7D%7B9x%5E2-4%7D)
Simplify,
![=\frac{(x+3)(3x+2)}{(3x-2)(3x+2)}-\frac{(x-3)(3x-2)}{(3x+2)(3x-2)}=\frac{44}{9x^2-4}\\\\=\frac{3x^2+11x+6}{9x^2-4}-\frac{3x^2-11x+6}{9x^2-4}=\frac{44}{9x^2-4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%28x%2B3%29%283x%2B2%29%7D%7B%283x-2%29%283x%2B2%29%7D-%5Cfrac%7B%28x-3%29%283x-2%29%7D%7B%283x%2B2%29%283x-2%29%7D%3D%5Cfrac%7B44%7D%7B9x%5E2-4%7D%5C%5C%5C%5C%3D%5Cfrac%7B3x%5E2%2B11x%2B6%7D%7B9x%5E2-4%7D-%5Cfrac%7B3x%5E2-11x%2B6%7D%7B9x%5E2-4%7D%3D%5Cfrac%7B44%7D%7B9x%5E2-4%7D)
Distribute the negative sign to simplify the left side of the equation;
![=\frac{3x^2+11x+6}{9x^2-4}-\frac{3x^2-11x+6}{9x^2-4}=\frac{44}{9x^2-4}\\\\=\frac{3x^2+11x+6-(3x^2-11x+6)}{9x^2-4}=\frac{44}{9x^2-4}\\\\=\frac{3x^2+11x+6-3x^2+11x-6}{9x^2-4}=\frac{44}{9x^2-4}\\\\=\frac{22x}{9x^2-4}{=\frac{44}{9x^2-4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3x%5E2%2B11x%2B6%7D%7B9x%5E2-4%7D-%5Cfrac%7B3x%5E2-11x%2B6%7D%7B9x%5E2-4%7D%3D%5Cfrac%7B44%7D%7B9x%5E2-4%7D%5C%5C%5C%5C%3D%5Cfrac%7B3x%5E2%2B11x%2B6-%283x%5E2-11x%2B6%29%7D%7B9x%5E2-4%7D%3D%5Cfrac%7B44%7D%7B9x%5E2-4%7D%5C%5C%5C%5C%3D%5Cfrac%7B3x%5E2%2B11x%2B6-3x%5E2%2B11x-6%7D%7B9x%5E2-4%7D%3D%5Cfrac%7B44%7D%7B9x%5E2-4%7D%5C%5C%5C%5C%3D%5Cfrac%7B22x%7D%7B9x%5E2-4%7D%7B%3D%5Cfrac%7B44%7D%7B9x%5E2-4%7D)
Since the denominators on opposite sides of the equation are like, one can now ignore the denominators,
![=22x=44](https://tex.z-dn.net/?f=%3D22x%3D44)
Inverse operations,
![=22x=44](https://tex.z-dn.net/?f=%3D22x%3D44)
÷
÷![2](https://tex.z-dn.net/?f=2)
![x=2](https://tex.z-dn.net/?f=x%3D2)
Answer: Transitive Postulate of Inequality (last option)
Explanation:
Let's say we have a vacation where we go from City A, to City B, then to City C. We can use the notation
. If all we cared about was the first and last cities, then we basically say
taking a shortcut so to speak.
This analogy is useful to describe the transitive property.
The equality version is where if we had a = b and b = c, then a = c.
The inequality version is where if we had a < b and b < c, then a < c. In this case, c = 2.
In a sense, its like linking together metal chains. A leads to B which leads to C. So we can just jump from A to C.
It might help to draw out a number line and pick values for a and b like a = 0 and b = 1. That way you can see how a < b, b < c and a < c all tie together.
Answer:
-<em>6</em>
Step-by-step explanation:
because it - + 18 + 17 + 19 + 20 answers
Domain is the x value. So you would just plug in every value in the domain set into the f(x) function.
5 (-2) + 4 =
-6
5 (3) + 4 =
19
5 (5) + 4 =
29
Your answer is B.