Final answer:
The equation 5w + 6 = –6(–9w – 1) + 15w has one unique solution, w = 0.
Step-by-step explanation:
The student asked: How many solutions does this equation have?
Let's solve the equation step by step:
5w + 6 = –6(–9w – 1) + 15w
Multiply through the parentheses:
5w + 6 = 54w + 6 + 15w
Combine like terms:
5w + 6 = 69w + 6
Subtract 5w from both sides:
6 = 64w + 6
Subtract 6 from both sides:
0 = 64w
Divide by 64:
w = 0
The equation has one unique solution, which is w = 0.