https://file.aiquickdraw.com/mathbot/file/1726470456253nd8ql0k7.jpg

The equation in the image is:

\[
\frac{5(3x + 2)}{2} = 1
\]

Let's solve for \(x\).

1. Multiply both sides by 2 to eliminate the denominator:
\[
5(3x + 2) = 2
\]

2. Expand the left side:
\[
15x + 10 = 2
\]

3. Subtract 10 from both sides:
\[
15x = 2 - 10
\]
\[
15x = -8
\]

4. Divide by 15:
\[
x = \frac{-8}{15}
\]

Thus, the solution is:
\[
x = \frac{-8}{15}
\]

Would you like any further details or have questions about this solution? Here are some related questions:

1. How can we check if the solution \(x = \frac{-8}{15}\) is correct?
2. What happens if the equation had a different constant on the right-hand side?
3. How does solving a similar equation with different coefficients affect the process?
4. What are the steps to solve equations involving fractions?
5. How would the solution change if the denominator were different?

**Tip:** Always aim to clear fractions early when solving equations to simplify your work.

Learn how to solve the linear equation 5(3x + 2)/2 = 1 step by step. This problem covers algebraic concepts including clearing fractions and solving linear equations. Suitable for students in Grades 8-10.

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