Answered

What is the solution to [tex]\frac{4}{x-3}+5=2[/tex]?

A. [tex]\frac{5}{3}[/tex]
B. [tex]-\frac{3}{5}[/tex]
C. [tex]\frac{3}{5}[/tex]
D. [tex]-\frac{5}{3}[/tex]



Answer :

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].