Question 89·Medium·Linear Equations in One Variable

Try subtracting $2(3y - 2)$ from both sides so that all the $3y - 2$ terms are on the same side of the equation.

Once you have something like $5(3y - 2) = 5(\text{something})$, divide both sides by 5, solve the resulting linear equation for $y$, and then plug that value into $3y - 2$—the expression the question asks for.

In Desmos, enter the left-hand side as one function and the right-hand side as another:

• Type f(y) = 7(3y - 2)
• Type g(y) = 5(y + 6) + 2(3y - 2) Then look for the intersection point of the graphs of $f$ and $g$; its $y$-coordinate is the value of $y$ that satisfies the equation.

Once you know the value of $y$ from the intersection, add a new line in Desmos and type 3*(value_of_y) - 2 (replacing value_of_y with the number you found). The output of this expression is the value of $3y - 2$ that you need for the answer choice.

Start with the equation:

Notice that $3y - 2$ appears on both sides. Subtract $2(3y - 2)$ from both sides to combine those terms on the left:

Now factor $3y - 2$ on the left:

So you get:

Both sides of the equation are multiplied by 5, so divide both sides by 5:

Now you have a simple linear equation relating $3y - 2$ and $y$.

Solve $3y - 2 = y + 6$:

• Subtract $y$ from both sides:

which simplifies to

• Add 2 to both sides:

• Divide both sides by 2:

Now substitute $y = 4$ into $3y - 2$:

So the value of $3y - 2$ is 10.