After you clear the denominator and distribute $s$, rearrange the equation so that all terms involving $t$ are on one side and all terms without $t$ are on the other side.

Once all t-terms are on one side, factor out $t$ from that side. Then divide both sides by the remaining factor to isolate $t$.

If you end up with extra negative signs, consider factoring out $-1$ from the numerator and/or denominator so that your final expression looks like one of the answer choices.

In Desmos, define the function of $t$ that gives $s$:

Type: f(t) = (5t - 1) / (2t + 3)

This represents the original equation $s = \dfrac{5t - 1}{2t + 3}$ as $f(t)$.

Choose a simple value for $s$ that does not make any denominator zero (for example, $s = 0$ or $s = 1$). In Desmos, define that value (e.g., s = 1). Then, for each answer choice, create an expression for $t$ using that $s$ value, such as t_A = (5s - 2) / (2 - 3s), t_B = (1 - 3s) / (5 + 2s), etc.

For each $t$ value you computed, evaluate f(t_A), f(t_B), f(t_C), and f(t_D) in Desmos. Compare each result to your chosen $s$ value. The correct formula for $t$ will be the one where f(t_choice) equals $s$ (and will continue to work if you try a second, different $s$ value). Match that successful formula with the corresponding answer choice.

Start with the given equation:

Multiply both sides by $2t + 3$ to eliminate the denominator:

Now distribute $s$ on the left:

We want all the terms involving $t$ on one side and the constant/$s$-only terms on the other.

Subtract $5t$ from both sides and subtract $3s$ from both sides:

Now factor $t$ out of the left side:

Divide both sides by $2s - 5$ to solve for $t$:

Factor $-1$ out of the numerator and denominator:

• Numerator: $-1 - 3s = -(1 + 3s)$
• Denominator: $2s - 5 = -(5 - 2s)$

So

Thus, the correct expression for $t$ in terms of $s$ is $t = \dfrac{1 + 3s}{5 - 2s}$, which matches choice D.