Question

Solve the proportion.



−
3
z
=
10
4
z
−3
​
=
4
10
​








z
=
z=

Answer 1

wrong

Answer 2

To solve the proportion \(-\frac{3}{z} = \frac{10}{4z - 3}\), we'll use cross-multiplication.

Cross-multiplying gives us:

\[
-3(4z - 3) = 10z
\]

Now, distribute \(-3\) on the left side:

\[
-12z + 9 = 10z
\]

Next, we'll move all terms involving \(z\) to one side and constant terms to the other side. To do this, add \(12z\) to both sides:

\[
9 = 10z + 12z
\]
\[
9 = 22z
\]

Now, divide both sides by \(22\) to solve for \(z\):

\[
z = \frac{9}{22}
\]

So, the solution is:

\[
z = \frac{9}{22}
\]

Answer 3

Let's go through the solution step-by-step again to solve the proportion correctly:

Given the equation:
\[
-\frac{3}{z} = \frac{10}{4z - 3}
\]

We'll use cross-multiplication:
\[
-3(4z - 3) = 10z
\]

Now, let's distribute the \(-3\) on the left side:
\[
-12z + 9 = 10z
\]

Next, we'll move all \(z\) terms to one side and constant terms to the other side:
Add \(12z\) to both sides:
\[
9 = 10z + 12z
\]
\[
9 = 22z
\]

Now, divide both sides by \(22\) to solve for \(z\):
\[
z = \frac{9}{22}
\]

Now, let’s ensure that this fraction is in its simplest form. Since 9 and 22 do not have any common factors other than 1, \(\frac{9}{22}\) is already simplified.

Thus, the correct answer is:
\[
z = \frac{9}{22}
\]

If there's a mistake or if you have a specific proportion to solve, please clarify, and I'll be glad to assist!