select the correct answer.\nit would take charlene and gina 18 minutes to organize charlenes comic - book…

select the correct answer.\nit would take charlene and gina 18 minutes to organize charlenes comic - book collection if they work together. if gina works alone, it would take her 15 minutes longer than it would take charlene working alone.\nwhen x represents the number of minutes it takes charlene to organize the comic - book collection working alone, the situation is represented by this equation:\n$\frac{1}{x}+\frac{1}{x + 15}=\frac{1}{18}$.\nwhich value is a solution of the rational equation that must be discarded because of the context?\na. $x = 0$\nb. $x=-9$\nc. $x=-15$\nd. $x=-30$

select the correct answer.\nit would take charlene and gina 18 minutes to organize charlenes comic - book collection if they work together. if gina works alone, it would take her 15 minutes longer than it would take charlene working alone.\nwhen x represents the number of minutes it takes charlene to organize the comic - book collection working alone, the situation is represented by this equation:\n$\frac{1}{x}+\frac{1}{x + 15}=\frac{1}{18}$.\nwhich value is a solution of the rational equation that must be discarded because of the context?\na. $x = 0$\nb. $x=-9$\nc. $x=-15$\nd. $x=-30$

Answer

Explanation:

Step1: Recall the context meaning

$x$ represents the time it takes Charlene to work alone, and time cannot be negative or zero in this real - world situation.

Step2: Analyze each option

  • Option A: $x = 0$ means Charlene takes 0 minutes to organize the collection alone, which is not possible in reality.
  • Option B: $x=-9$ is a negative value for time, which is not valid as time cannot be negative in the context of work - time problems.
  • Option C: $x = - 15$ is also a negative value for time, not valid.
  • Option D: $x=-30$ is a negative value for time, not valid. But among these non - valid values, we are looking for a solution of the rational equation. First, we solve the rational equation $\frac{1}{x}+\frac{1}{x + 15}=\frac{1}{18}$. Multiply through by $18x(x + 15)$ to get $18(x + 15)+18x=x(x + 15)$. Expand: $18x+270+18x=x^{2}+15x$. Rearrange to $x^{2}-21x - 270=0$. Factor: $(x - 30)(x+9)=0$. The solutions of the equation are $x = 30$ and $x=-9$. Since $x$ represents time, the value $x=-9$ must be discarded because time cannot be negative.

Answer:

B. $x=-9$