After distributing, combine like terms on the left side (group the $y$-terms together and the constant numbers together), then start moving variable terms to one side and constants to the other.

Once you get a simple equation like $3y = 2$, think about how to turn it into an equation involving $9y$ and then $9y + 1$, instead of first solving for $y$ as a fraction.

In Desmos, use $x$ as the variable. In one line, enter f(x) = 5(4x + 2) - 3(2x - 4). In another line, enter g(x) = 8x + 26. These represent the left and right sides of the equation.

Look for the intersection point of the graphs of $f$ and $g$. The $x$-coordinate of this intersection is the value that makes the original equation true (this is the same as the $y$-value in the problem statement). Note this $x$-value.

In a new line, type 9*(value) + 1, replacing value with the $x$-coordinate you found at the intersection (for example, if the intersection is at $x = a$, type 9*a + 1). The number Desmos outputs is the value of $9y + 1$; compare this with the answer choices.

Use the distributive property on both grouped terms.

• Multiply $5$ by each term in $(4y+2)$.
• Multiply $-3$ by each term in $(2y-4)$.

This gives

So the equation becomes

Combine the $y$-terms and the constants on the left:

• $20y - 6y = 14y$
• $10 + 12 = 22$

So the equation simplifies to

Move all $y$-terms to one side and constants to the other.

Subtract $8y$ from both sides:

Now subtract $22$ from both sides:

Divide both sides by $2$ to get a simpler equation:

You want $9y + 1$, and you already know that $3y = 2$.

Multiply both sides of $3y = 2$ by $3$ to get an equation for $9y$:

Now add $1$ to both sides to match the expression $9y + 1$:

So $9y + 1 = 7$, which corresponds to answer choice C) 7.