9514 1404 393
Answer:
x = 2/3
Step-by-step explanation:
The approach usually recommended for almost any problem involving fractions is to "clear fractions" first. Here, that means multiplying both sides of the equation by 2x (the least common denominator). After that, divide both sides by the coefficient of x.
[tex]\dfrac{2}{x}=\dfrac{6}{2}\qquad\text{given}\\\\\dfrac{(2x)(2)}{x}=\dfrac{(2x)(6)}{2}\qquad\text{multiply by $2x$}\\\\4=6x\qquad\text{simplify}\\\\\dfrac{4}{6}=x\qquad\text{divide by 6}\\\\\boxed{x=\dfrac{2}{3}}\qquad\text{reduce the fraction}[/tex]
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After you have done this a few times, you recognize that the process involves multiplying the original equation by 2x/6 = x/3. This is x times the reciprocal of the constant term on the right. You can "cut to the chase" and do multiplication of both sides by x/3 as your first step:
[tex]\dfrac{2}{x}\cdot\dfrac{x}{3}=\dfrac{6}{2}\cdot\dfrac{x}{3}\qquad\text{multiply the given equation by $\dfrac{x}{3}$}\\\\\dfrac{2}{3}=x\qquad\text{simplify}[/tex]
