https://file.aiquickdraw.com/mathbot/file/17282675372029c6jgrq1.jpg

The equation you have uploaded is:

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

Let me solve it step by step:

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 2 to eliminate the fraction:

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

This simplifies to:

\[
8 = 5(3x + 8)
\]

### Step 2: Distribute the 5 on the right side
Distribute the 5 to both terms inside the parentheses:

\[
8 = 5 \times 3x + 5 \times 8
\]

\[
8 = 15x + 40
\]

### Step 3: Isolate the variable term
Subtract 40 from both sides of the equation to isolate the term involving \(x\):

\[
8 - 40 = 15x
\]

\[
-32 = 15x
\]

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

\[
x = \frac{-32}{15}
\]

So, the solution to the equation is:

\[
x = \frac{-32}{15}
\]

Would you like more details or further clarification on any step? 

### Related Questions:
1. How do you solve equations with fractions in more complex scenarios?
2. What is the importance of isolating the variable when solving equations?
3. How do you handle equations with multiple variables?
4. What happens if the equation contains decimals instead of fractions?
5. How do you verify the solution to an algebraic equation?

### Tip:
When solving equations involving fractions, multiplying through by the least common denominator is a great way to eliminate the fractions early in the process, simplifying the equation.

Learn how to solve the linear equation 4 = (5/2)(3x + 8) step by step. This solution demonstrates key algebraic concepts, including the distributive property and isolating the variable. Suitable for students in Grades 8-10.

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