1/3(6x-9)-10+6x<35

To solve the inequality \( \frac{1}{3}(6x - 9) - 10 + 6x < 35 \), we can follow these steps:

1. Distribute \( \frac{1}{3} \) to the terms inside the parentheses: \[ \frac{1}{3}(6x) - \frac{1}{3}(9) - 10 + 6x < 35 \] This simplifies to: \[ 2x - 3 - 10 + 6x < 35 \]

2. Combine like terms: \[ 2x + 6x - 3 - 10 < 35 \] So, \[ 8x - 13 < 35 \]

3. Add \( 13 \) to both sides: \[ 8x < 35 + 13 \] Thus, \[ 8x < 48 \]

4. Divide both sides by \( 8 \): \[ x < 6 \]

The solution to the inequality is: \[ \boxed{x < 6} \]

Let’s double-check the solution step by step:

Given the inequality: \[ \frac{1}{3}(6x - 9) - 10 + 6x < 35 \]

1. Distribute \( \frac{1}{3} \): \[ \frac{1}{3}(6x) - \frac{1}{3}(9) - 10 + 6x < 35 \] This simplifies to: \[ 2x - 3 - 10 + 6x < 35 \]

2. Combine like terms: \[ 2x + 6x - 3 - 10 < 35 \] This simplifies to: \[ 8x - 13 < 35 \]

3. Add \( 13 \) to both sides: \[ 8x - 13 + 13 < 35 + 13 \] This simplifies to: \[ 8x < 48 \]

4. Divide both sides by \( 8 \): \[ x < \frac{48}{8} \] Thus, we find: \[ x < 6 \]

So the final conclusion is correct: \[ \boxed{x < 6} \]

Thank you for your patience, and the solution is indeed confirmed.