Solve -5(3x-7)+11=1. Justify each step with an operation or property

Solution:
1. Start with the equation:
-5(3x - 7) + 11 = 1

2. Distribute -5 across the terms inside the parentheses:
-5 \cdot 3x + -5 \cdot (-7) + 11 = 1

3. Simplify the expression:
-15x + 35 + 11 = 1

4. Combine like terms (constants):
-15x + 46 = 1

5. Subtract 46 from both sides for isolation of terms with x:
-15x + 46 - 46 = 1 - 46
-15x = -45

6. Divide both sides by -15 to solve for x:
x = \frac{-45}{-15}

7. Simplify the right side:
x = 3