https://file.aiquickdraw.com/mathbot/file/1725462411553cilzsynd.jpg

The given equation is:

\[
\frac{5}{8}x + \frac{1}{3}x = 46
\]

To solve for \( x \), let's follow these steps:

### Step 1: Combine the fractions

Combine the terms involving \( x \) by finding a common denominator for \(\frac{5}{8}\) and \(\frac{1}{3}\). The least common denominator (LCD) of 8 and 3 is 24.

Rewrite each fraction with the common denominator:

\[
\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}, \quad \frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}
\]

Now, combine these fractions:

\[
\frac{15}{24}x + \frac{8}{24}x = \frac{23}{24}x
\]

### Step 2: Set up the equation

Now, rewrite the equation with the combined fraction:

\[
\frac{23}{24}x = 46
\]

### Step 3: Solve for \( x \)

Multiply both sides by the reciprocal of \(\frac{23}{24}\):

\[
x = 46 \times \frac{24}{23}
\]

Simplify:

\[
x = \frac{46 \times 24}{23} = 2 \times 24 = 48
\]

So, the solution is:

\[
\boxed{x = 48}
\]

Would you like further details, or do you have any questions? Here are some related questions you might find interesting:

1. How do you solve equations involving multiple fractions?
2. What are common techniques for finding a common denominator?
3. How do you simplify complex fractions?
4. What are some real-life applications of solving fractional equations?
5. How can equations like this one be represented graphically?

**Tip:** Always double-check your fraction operations, especially when combining terms with different denominators, to avoid errors.

Solve the equation \(\frac{5}{8}x + \frac{1}{3}x = 46\)

Learn how to solve the linear equation \(\frac{5}{8}x + \frac{1}{3}x = 46\) by combining fractions and solving for \(x\). This problem is suitable for students in Grades 7-9 and covers key algebraic concepts, including working with fractions and solving linear equations.

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