Solve and determine if the equation has one, none or infinite soultions

Question

-5(x-1)=5-5x

Answer 1

To solve the equation \(-5(x-1) = 5 - 5x\), we'll start by distributing on the left side:

\[ -5(x - 1) = -5x + 5 \]

So the equation becomes:

\[ -5x + 5 = 5 - 5x \]

Next, we can simplify both sides. Both sides have \(-5x\), so we can add \(5x\) to both sides to eliminate that term:

\[ 5 = 5 \]

This statement is always true. Therefore, the equation does not involve any variables at this point, indicating that it is true for all values of \(x\).

This implies that the equation has infinitely many solutions, as any value of \(x\) will satisfy the equation.

Final Answer: The equation has infinitely many solutions.

Answer 2

Solve and determine if the equation has one, none or infinite soultions
12+4n=4(n+3

Answer 3

To solve the equation \(12 + 4n = 4(n + 3)\), let's start by distributing on the right side:

\[ 4(n + 3) = 4n + 12 \]

Now, rewrite the entire equation:

\[ 12 + 4n = 4n + 12 \]

Next, let's subtract \(4n\) from both sides:

\[ 12 = 12 \]

This statement is always true, indicating that the equation does not involve any variables. Thus, the equation holds for all values of \(n\).

This means that the equation has infinitely many solutions.

Final Answer: The equation has infinitely many solutions.