https://file.aiquickdraw.com/mathbot/file/1725843175433jq7hgqsy.jpg

The equation in the image is:

\[
3x + 9 = \frac{1}{2}x + \frac{5}{3}
\]

To solve for \(x\), let's go through the steps:

### Step 1: Eliminate the fractions
We can multiply the entire equation by the least common denominator (LCD) to remove the fractions. The LCD between 2 and 3 is 6. So, multiply the whole equation by 6:

\[
6(3x + 9) = 6\left(\frac{1}{2}x + \frac{5}{3}\right)
\]

This simplifies to:

\[
18x + 54 = 3x + 10
\]

### Step 2: Move all terms involving \(x\) to one side
Now, subtract \(3x\) from both sides:

\[
18x - 3x + 54 = 10
\]

This simplifies to:

\[
15x + 54 = 10
\]

### Step 3: Isolate the term with \(x\)
Subtract 54 from both sides:

\[
15x = 10 - 54
\]

\[
15x = -44
\]

### Step 4: Solve for \(x\)
Divide both sides by 15:

\[
x = \frac{-44}{15}
\]

So, the solution is:

\[
x = \frac{-44}{15}
\]

Would you like more details or have any questions?

Here are 5 related questions to expand this topic:
1. How do you solve a system of equations involving fractions?
2. What are the steps to find the least common denominator in an equation?
3. Can you solve an equation by factoring instead of eliminating fractions?
4. What is the process for solving inequalities with fractions?
5. How do you check if a solution to an equation is correct?

**Tip:** When solving equations with fractions, always consider clearing the fractions early by multiplying through by the least common denominator. This simplifies the process significantly!

Solve the equation: 3x + 9 = (1/2)x + 5/3

Explore the detailed solution to the linear equation 3x + 9 = (1/2)x + 5/3. Learn the steps to eliminate fractions and solve for x. Suitable for students in Grades 8-10, covering essential algebraic concepts.

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