Solve for the variable. Determine if there is one solution, infinitely many solutions, or no solution.-20d – 15 = -5(4d + 3)

1. Break Down the Problem

We need to solve the equation: $-20d - 15 = -5(4d + 3)$ First, we'll simplify the right side of the equation.

2. Relevant Concepts

To simplify, we can distribute $-5$ on the right side: $-5(4d + 3) = -5 \times 4d - 5 \times 3 = -20d - 15$ Now we have: $-20d - 15 = -20d - 15$

3. Analysis and Detail

Next, let's analyze the equation:

1. When we move all terms to one side, we have: $-20d - 15 + 20d + 15 = 0$
2. Simplifying, we see that: $0 = 0$ This indicates that the original equation holds true for any value of $d$.

4. Verify and Summarize

Since the equation simplifies to $0 = 0$, there are infinitely many solutions because the left side and the right side are identical for all values of $d$.

Final Answer

There are infinitely many solutions for the equation $-20d - 15 = -5(4d + 3)$.