https://file.aiquickdraw.com/mathbot/file/1726470521485z2t0zhvk.jpg

The equation provided in the image is:

\[
\frac{3}{2}x + 2x = \frac{5}{8}
\]

Let's solve this step by step:

### Step 1: Combine like terms
The terms involving \( x \) are \( \frac{3}{2}x \) and \( 2x \). To combine them, we need to express \( 2x \) with a denominator of 2:

\[
2x = \frac{4}{2}x
\]

So, the equation becomes:

\[
\frac{3}{2}x + \frac{4}{2}x = \frac{5}{8}
\]

Now combine the terms on the left-hand side:

\[
\frac{7}{2}x = \frac{5}{8}
\]

### Step 2: Solve for \( x \)
To solve for \( x \), multiply both sides of the equation by the reciprocal of \( \frac{7}{2} \), which is \( \frac{2}{7} \):

\[
x = \frac{5}{8} \times \frac{2}{7}
\]

Multiply the fractions:

\[
x = \frac{5 \times 2}{8 \times 7} = \frac{10}{56}
\]

Simplify the fraction:

\[
x = \frac{5}{28}
\]

Thus, the solution is:

\[
x = \frac{5}{28}
\]

Would you like more details on any of the steps? Here are a few related questions to consider:

1. What is the general method for solving equations with fractions?
2. How do you combine like terms in an equation?
3. Can you explain how to multiply fractions?
4. What is the process for simplifying fractions?
5. How do you handle equations where the variable is in multiple terms?

**Tip:** When solving equations with fractions, it’s often helpful to find a common denominator early on to combine terms more easily.

Solve the equation: \(\frac{3}{2}x + 2x = \frac{5}{8}\)

This detailed step-by-step guide shows how to solve the linear equation with fractions: 3/2x + 2x = 5/8. Learn how to combine like terms, multiply fractions, and simplify the solution. Suitable for students in Grades 7-9.

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