After distributing, collect the $z$-terms together on each side and the constant numbers together, so the equation is easier to work with.

Once you have an equation like $az + b = cz + d$, move all $z$ terms to one side and the constants to the other to find $z$. Then remember the question asks for $4z$, so multiply your $z$ value by 4.

In Desmos, type y1 = 5(2x + 1) - 3x and on a new line type y2 = 2(4x + 7). Here, $x$ in Desmos plays the role of $z$ in the problem.

Click on the point where the graphs of $y1$ and $y2$ intersect. The $x$-coordinate of this intersection is the solution for $z$.

In a new expression line, type 4 * followed by the $x$-value you found (or use a Desmos variable if you stored it). The value Desmos shows for this expression is the value of $4z$.

Start with the given equation:

Distribute the 5 on the left:

• $5 \cdot 2z = 10z$
• $5 \cdot 1 = 5$

So the left side becomes $10z + 5 - 3z$.

Distribute the 2 on the right:

• $2 \cdot 4z = 8z$
• $2 \cdot 7 = 14$

So the right side becomes $8z + 14$.

Now the equation is:

On the left side, combine the $z$-terms:

• $10z - 3z = 7z$

So the equation becomes:

Now we have a simpler linear equation with $z$ on both sides.

To get all the $z$ terms on one side, subtract $7z$ from both sides:

Now subtract 14 from both sides to isolate $z$:

So $z = -9$.

We are asked for $4z$, not just $z$.

Multiply $z$ by 4:

So the value of $4z$ is $-36$.