Question

If $y=2x+2/x$ and $x=3$ then $y$ is: (A) $10/3$ (B) $18/3$ (C) $8^2/3$ (D) $20/3$ (E) None of the above

Short answer

Option (D) $\frac{20}{3}$

Step-by-step solution

- Substitute the value of x

Substitute the given value of $x=3$ into the equation $y=2x+\frac{2}{x}$.

- Perform the substitutions

Using the value $x=3$, we get: $$y=2(3)+\frac{2}{3}$$

- Simplify the expression

Calculate the values: $$2(3)=6\text{ and }\frac{2}{3}=\frac{2}{3}$$. Now combine them: $$y=6+\frac{2}{3}=\frac{18}{3}+\frac{2}{3}=\frac{20}{3}$$

- Verify and select answer

The value of $y$ is $\frac{20}{3}$, which matches option (D).

Key concepts

algebraic equations

Algebraic equations are mathematical statements that show the equality between two expressions. They often contain variables, which are symbols representing unknown values. In our exercise, the equation is given by$y=2x+\frac{2}{x}$. This specific equation expresses a relation where $y$ depends on the value of $x$. Understanding how to work with algebraic equations is crucial in solving many math problems. To solve for $y$, we need to substitute the value of $x$ with the number provided.

substitution method

The substitution method involves replacing a variable with a given value to simplify an equation. In our example, we are given $x=3$. By substituting $x$ in the equation $y=2x+\frac{2}{x}$, we replace every instance of $x$ with the number 3. Our equation then becomes: $y=2(3)+\frac{2}{3}$. This method allows for the equation to be simplified step-by-step. It is a straightforward and effective technique for finding the value of the other variable.

simplifying expressions

Simplifying expressions means reducing them to their most basic form. This process helps to find the value more easily. In the given problem, the expression $2(3)+\frac{2}{3}$ is simplified as follows: Calculate $$2(3)=6$$ and $\frac{2}{3}$ remains $\frac{2}{3}$. Combining these, we get $y=6+\frac{2}{3}$. Further simplify by combining the fractions: $y=\frac{18}{3}+\frac{2}{3}=\frac{20}{3}$. Simplifying makes complex problems more manageable and helps in accurately finding the solutions.