After you clear the fractions, you will still have parentheses. Simplify the expression inside $\left(2-\dfrac{3x-4}{2}\right)$ first, then distribute the numbers in front of each set of parentheses.

Once everything is expanded, group the constant terms together and the $x$ terms together. Then move all the $x$ terms to one side of the equation and the constants to the other side before dividing to solve for $x$.

In Desmos, type the left side as y1 = 5/3(2-(3x-4)/2)+1/4(x+6) and the right side as y2 = 7-5x/6. This will graph each side of the equation as a separate line.

Zoom or pan until you see where the graphs of $y_1$ and $y_2$ cross. Tap the intersection point; the $x$-coordinate shown there is the solution to the equation.

Start with the original equation:

The denominators are 3, 2, 4, and 6. The least common multiple of these is 12, so multiplying every term by 12 will clear all the fractions.

Multiply each term on both sides by 12:

Now simplify the coefficients:

• $12\cdot\frac{5}{3}=20$
• $12\cdot\frac{1}{4}=3$
• $12\cdot 7=84$
• $12\cdot\frac{5x}{6}=10x$

So the equation becomes:

First simplify $2-\dfrac{3x-4}{2}$:

• Write $2$ as $\dfrac{4}{2}$, so

• Then $20\left(2-\dfrac{3x-4}{2}\right)=20\cdot\dfrac{8-3x}{2}=10(8-3x)=80-30x$.
• Also, $3(x+6)=3x+18$.

Substitute these into the equation:

On the left side, combine like terms:

• Constants: $80+18=98$
• $x$ terms: $-30x+3x=-27x$

So the equation becomes:

Now solve step by step:

• Subtract 84 from both sides: $98-84-27x=-10x$, so $14-27x=-10x$.
• Add $27x$ to both sides: $14=17x$.
• Divide both sides by 17: $x=\dfrac{14}{17}$.

So the solution is $x=\dfrac{14}{17}$, which corresponds to choice D.