How many solutions does each of the following equations have?
$0.25x+0.6=0.25(x+3)$

• A. One solution
• B. Infinite solutions
• C. No solution

Answer: (C)

Verified step by step guidance

1. Start by writing down the given equation: \(0.25x + 0.6 = 0.25\left(x + 3\right)\).
2. Distribute the \$0.25$ on the right side to both terms inside the parentheses: \(0.25x + 0.6 = 0.25x + 0.25 \times 3\).
3. Simplify the right side multiplication: \$0.25x + 0.6 = 0.25x + 0.75$.
4. Next, subtract \$0.25x\( from both sides to try to isolate the variable terms: \)0.25x - 0.25x + 0.6 = 0.25x - 0.25x + 0.75\(, which simplifies to \)0.6 = 0.75$.
5. Since \$0.6\( does not equal \)0.75\(, this is a contradiction, meaning there is no value of \)x$ that satisfies the equation, so the equation has no solution.