Use cross multiplication to solve the following proportion:
2
x
−
3
10
=
3
x
+
2
12
.
 
Write your answer as a simplified fraction.

We are given the proportion:

\[
\frac{2x - 3}{10} = \frac{3x + 2}{12}
\]

To solve this using cross multiplication, we multiply the numerator of one fraction by the denominator of the other and set the products equal to each other:

\[
(2x - 3) \cdot 12 = (3x + 2) \cdot 10
\]

Now, let's distribute both sides:

\[
12(2x - 3) = 10(3x + 2)
\]

Expanding both sides:

\[
24x - 36 = 30x + 20
\]

Next, we move all terms involving \(x\) to one side and constants to the other side. First, subtract \(24x\) from both sides:

\[
-36 = 6x + 20
\]

Now subtract 20 from both sides:

\[
-56 = 6x
\]

Finally, solve for \(x\) by dividing both sides by 6:

\[
x = \frac{-56}{6} = \frac{-28}{3}
\]

Thus, the solution is:

\[
x = \frac{-28}{3}
\]

Would you like more details or have any questions?

---

Here are 5 related questions to consider:
1. What is the process for solving a proportion with more complex expressions?
2. How would the solution change if one side of the equation had a negative denominator?
3. Can cross multiplication be used to solve any proportion?
4. What is the next step if the terms cannot be simplified after cross multiplication?
5. How do you verify the solution after solving a proportion?

**Tip:** Always double-check your distribution when dealing with cross multiplication to avoid errors in expanding terms.

Use cross multiplication to solve the following proportion: (2x - 3)/10 = (3x + 2)/12. Write your answer as a simplified fraction.

Discover how to solve the proportion (2x - 3)/10 = (3x + 2)/12 using cross multiplication. Follow a detailed step-by-step solution, perfect for students in Grades 8-10, and learn essential algebraic concepts including linear equations and proportion solving techniques.

Math Problem Statement

Use cross multiplication to solve the following proportion: 2 x − 3 10

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