To solve the equation [tex]\(\frac{4}{x-3} + 5 = 2\)[/tex], let's follow the steps:
1. Isolate the fraction term:
[tex]\[\frac{4}{x-3} = 2 - 5\][/tex]
Simplify the right hand side:
[tex]\[\frac{4}{x-3} = -3\][/tex]
2. Eliminate the fraction by multiplying both sides by the denominator [tex]\((x-3)\)[/tex]:
[tex]\[4 = -3(x-3)\][/tex]
3. Simplify the equation:
Distribute [tex]\(-3\)[/tex] on the right hand side:
[tex]\[4 = -3x + 9\][/tex]
4. Isolate the variable [tex]\(x\)[/tex]:
Subtract 9 from both sides to move the constant term to the left:
[tex]\[4 - 9 = -3x\][/tex]
Simplify the left hand side:
[tex]\[-5 = -3x\][/tex]
5. Solve for [tex]\(x\)[/tex] by dividing both sides by [tex]\(-3\)[/tex]:
[tex]\[x = \frac{-5}{-3}\][/tex]
Simplify the division:
[tex]\[x = \frac{5}{3}\][/tex]
The solution to the equation [tex]\(\frac{4}{x-3} + 5 = 2\)[/tex] is [tex]\(x = \frac{5}{3}\)[/tex].
Given the choices:
A. [tex]\(\frac{5}{3}\)[/tex]
B. [tex]\(-\frac{3}{5}\)[/tex]
C. [tex]\(\frac{3}{5}\)[/tex]
D. [tex]\(-\frac{5}{3}\)[/tex]
The correct answer is A. [tex]\(\frac{5}{3}\)[/tex].
