Question

What is the easiest way to solve this problem? thank u!!

Answer 1

Answer:

  B.  2

Step-by-step explanation:

You can add 1/(x+5), then multiply by (x+5), then subtract (x+3).

$\dfrac{2(x+1)+1}{x+5}=1 \qquad\text{add 1/(x+5)}\\\\2x+3=x+5 \qquad\text{multiply by x+5}\\\\x=2 \qquad\text{subtract x+3}}$

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Sometimes you have to try several methods to find the easiest. One "always works" method is to subtract one side of the equation so you have something that equals zero. Here that would look like ...

$\dfrac{2(x+1)}{x+5}-1+\dfrac{1}{x+5}=0 \qquad\text{subtract the right side}\\\\\dfrac{2(x+1)-(x+5)+1}{x+5}=0 \qquad\text{use a common denominator}\\\\\dfrac{x-2}{x+5}=0 \qquad\text{simplify}\\\\x=2 \qquad\text{the value of x that makes the numerator 0}$

Answer 2

Answer:

B. 2

Step-by-step explanation:

$\frac{2(x + 1)}{x + 5} = 1 - \frac{1}{x + 5}$

Multiply two sides by (x+5), we have

$(x + 5) \frac{2(x + 1)}{x + 5} = (x + 5) - (x + 5) \frac{1}{x + 5}$

so

$2(x + 1) = x + 5 - 1 \\ = > \: 2x + 2 = x + 4 \\ = > x = 2$