Question

The sum of two times a number and three is equal to eleven times the number. Find the number.

• A. $3$
• B. $-\frac{1}{3}$
• C. $\frac{1}{3}$
• D. $-3$

Answer 1

The correct option is C $\frac{1}{3}$

Let the number be $x,$ then the sum of two times $x$ and three is equal to eleven times $x$.
$\Rightarrow 2x+3=11x$

Step 1: Subtract both sides of the equation by 3 to eliminate 3 on the left side of the equation.
$\Rightarrow 2x+3-3=11x-3\Rightarrow 2x=11x-3$

Step 2: Subtract both sides of the equation by $11x$ to eliminate $11x$ on the right side of the equation.
$\Rightarrow 2x-11x=11x-3-11x$
$\Rightarrow -9x=-3$

Step 3: Now, divide both sides by -9 to eliminate -9 on the left side of the equation.
$\Rightarrow \frac{-9x}{-9}=\frac{-3}{-9}\Rightarrow x=\frac{1}{3}$

Hence, the required number is $\frac{1}{3}.$