We can solve the equation step by step:

Given equation:  
\[
x - \frac{5}{3} + 9 = 12
\]

### Step 1: Combine like terms on the left-hand side.
First, combine the constants \(9\) and \( - \frac{5}{3}\):

\[
x + \left( 9 - \frac{5}{3} \right) = 12
\]

Convert 9 to a fraction with the same denominator as \(\frac{5}{3}\):

\[
9 = \frac{27}{3}
\]

Now subtract:

\[
x + \frac{27}{3} - \frac{5}{3} = 12
\]

\[
x + \frac{22}{3} = 12
\]

### Step 2: Isolate \(x\).
To isolate \(x\), subtract \(\frac{22}{3}\) from both sides:

\[
x = 12 - \frac{22}{3}
\]

Convert 12 to a fraction with the same denominator:

\[
12 = \frac{36}{3}
\]

Now subtract:

\[
x = \frac{36}{3} - \frac{22}{3} = \frac{14}{3}
\]

Thus, the solution is:

\[
x = \frac{14}{3}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you handle equations involving fractions?
2. Can you solve for \(x\) in \(x + \frac{7}{2} - 4 = 0\)?
3. How do you solve equations involving multiple fractions on both sides?
4. How can you check if your solution to an equation is correct?
5. Can we solve \(2x - \frac{1}{5} + 3 = \frac{6}{5}\)?

**Tip**: When dealing with fractions, it's often helpful to find a common denominator to simplify the arithmetic.

Learn how to solve the linear equation x - 5/3 + 9 = 12 with a step-by-step solution. This problem covers algebraic concepts, including handling fractions and isolating variables. Suitable for students in Grades 6-8.

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