https://file.aiquickdraw.com/mathbot/file/1727025253407370mbtso.jpg

The equation provided in the image is:

\[
\frac{x + 3}{x - 1} = \frac{5}{9}
\]

To solve this equation, we can use cross-multiplication to eliminate the fractions. Let's go step-by-step:

### Step 1: Cross-multiply
\[
9(x + 3) = 5(x - 1)
\]

### Step 2: Expand both sides
Expand the expressions on both sides:

\[
9x + 27 = 5x - 5
\]

### Step 3: Move all terms involving \(x\) to one side
Subtract \(5x\) from both sides:

\[
9x - 5x + 27 = -5
\]

\[
4x + 27 = -5
\]

### Step 4: Isolate \(x\)
Subtract 27 from both sides:

\[
4x = -5 - 27
\]

\[
4x = -32
\]

### Step 5: Solve for \(x\)
Divide both sides by 4:

\[
x = \frac{-32}{4} = -8
\]

### Final Solution:
\[
x = -8
\]

Let me know if you'd like a further breakdown or if you have any questions! Here are five related questions to practice:

1. How do you solve a quadratic equation?
2. What happens if both sides of the equation contain fractions with different denominators?
3. Can cross-multiplication be used for equations with more complex denominators?
4. How can you check if a solution is valid for a rational equation?
5. What happens if the denominator of a rational equation equals zero?

**Tip:** Always check the solution by substituting it back into the original equation to ensure it's correct.

Solve the equation: (x + 3) / (x - 1) = 5 / 9

Learn how to solve the rational equation (x + 3) / (x - 1) = 5 / 9 using cross-multiplication. This step-by-step guide walks you through the algebraic process, including simplifying and isolating variables. Suitable for Grades 7-9 students looking to strengthen their algebra skills.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation