https://file.aiquickdraw.com/mathbot/file/17267572632794yuym3c5.jpg

The equation provided in the image is:

\[
\frac{4x}{5} = \frac{x + 3}{6}
\]

We will solve for \( x \) step by step:

### Step 1: Eliminate the fractions by multiplying both sides by the least common denominator (LCD) of 5 and 6, which is 30.

\[
30 \cdot \frac{4x}{5} = 30 \cdot \frac{x + 3}{6}
\]

This simplifies to:

\[
6 \cdot 4x = 5 \cdot (x + 3)
\]

### Step 2: Simplify both sides.

\[
24x = 5(x + 3)
\]

### Step 3: Distribute the 5 on the right side.

\[
24x = 5x + 15
\]

### Step 4: Move all the terms involving \( x \) to one side of the equation.

\[
24x - 5x = 15
\]

\[
19x = 15
\]

### Step 5: Solve for \( x \) by dividing both sides by 19.

\[
x = \frac{15}{19}
\]

Thus, the value of \( x \) is:

\[
\boxed{\frac{15}{19}}
\]

This corresponds to the fourth option.

Would you like further explanation or have additional questions?

### Related Questions:
1. How would the solution change if the equation were \(\frac{4x}{5} = \frac{x - 3}{6}\)?
2. What is the LCD of 5 and 8, and how would you use it in solving equations with these denominators?
3. How do you check your solution to ensure \( x = \frac{15}{19} \) is correct?
4. How can we solve \(\frac{4x}{5} + 2 = \frac{x + 3}{6}\)?
5. How do you solve an equation with more than two fractions on each side?

### Tip:
Always eliminate fractions early by multiplying through by the least common denominator—it simplifies the entire process!

What is the value of x when (4x / 5) = (x + 3) / 6?

This page provides a step-by-step solution to the algebraic equation 4x/5 = (x + 3)/6. Learn how to eliminate fractions, distribute terms, and solve for x. This problem is suitable for students in Grades 8-10.

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