https://file.aiquickdraw.com/mathbot/file/1727958054202p3deje69.jpg

The equation given in the image is:

\[
\frac{12}{2 - x} = \frac{1}{3x + 8}
\]

We will solve this step-by-step:

### Step 1: Cross-multiply
To eliminate the fractions, cross-multiply:

\[
12(3x + 8) = 1(2 - x)
\]

This simplifies to:

\[
12(3x + 8) = 2 - x
\]

### Step 2: Expand both sides
Now, expand both sides of the equation:

\[
36x + 96 = 2 - x
\]

### Step 3: Move all terms involving \(x\) to one side
Add \(x\) to both sides to collect the \(x\)-terms together:

\[
36x + x + 96 = 2
\]

Simplifies to:

\[
37x + 96 = 2
\]

### Step 4: Isolate \(x\)
Subtract 96 from both sides:

\[
37x = 2 - 96
\]

\[
37x = -94
\]

### Step 5: Solve for \(x\)
Divide both sides by 37:

\[
x = \frac{-94}{37}
\]

This simplifies to:

\[
x = -\frac{94}{37}
\]

\[
x = -2.54 \, \text{(approximately)}
\]

### Solution:
The solution to the equation is \( x \approx -2.54 \).

Would you like more details on any of these steps or have any questions?

---

Here are some related questions you can try:

1. What happens if we modify the denominator on the left-hand side to \(2 + x\)?
2. How would you solve this if both fractions had quadratic terms?
3. Can you find the solution if the equation was \( \frac{12}{2 - x} = \frac{2}{3x + 8} \)?
4. What would happen if the right-hand side was \( \frac{1}{3x - 8} \)?
5. How would you solve this equation graphically?

**Tip**: When solving fractional equations, cross-multiplying is a powerful way to eliminate the fractions and simplify the problem.

Solve the equation 12/(2 - x) = 1/(3x + 8)

Step-by-step solution to solve the rational equation 12/(2 - x) = 1/(3x + 8), involving cross-multiplication and algebraic manipulation. Ideal for students in grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation