Question 431·Hard·Algebra

Type the equation below, changing every $x$ to $x_1$ and $=$ to $\sim$. Desmos uses $x$ for graphing; the regression sign $\sim$ tells it to find the value of $x_1$ that makes both sides equal. Under PARAMETERS, it shows $x_1=5.333333\ldots$. Keep $2x_1+5$ together in the numerator so the minus sign subtracts the whole fraction.

Type $x_1$ on a new line. Desmos displays its decimal value; press that line's fraction button to display $\frac{16}{3}$. Since $x_1$ stands for the equation's $x$, the value that satisfies the equation is $x=\frac{16}{3}$. Choice B.

The denominators are the bottom numbers $6$, $3$, and $2$. Multiply every term on both sides by $6$, which each denominator divides into:

Distribute $-2$ to both terms inside $2x+5$; don't change only the $2x$ term: $4x-7-4x-10=3(x-11)$. The minus sign reaches the $5$, too.

Combine like terms, which have the same variable part, and combine the plain numbers: $-17=3(x-11)$. The $4x$ and $-4x$ cancel, so the whole left side is a constant.

Distribute $3$ to both terms inside $x-11$: $-17=3x-33$. The $3$ multiplies $-11$ as well as $x$.

Add $33$ to both sides to keep the equation equal:

Divide both sides by $3$: $\frac{16}{3}=x$. So $x=\frac{16}{3}$ satisfies the equation. Choice B.