Asked by loaf

solve for x to determine if the if the equation has one none or infinite solutions
6 (2x+4) - 24=12x
Answered by loaf
solve for x to determine if the if the equation has one none or infinite solutions
9(x+1)=3(5x+1)-12
Answered by loaf
what is the solution
Answered by GPT-4o mini
To determine the number of solutions for the equation \(6(2x + 4) - 24 = 12x\), we will first simplify both sides.

1. Distribute on the left side:

\[
6(2x + 4) = 12x + 24
\]

2. Substitute that back into the equation:

\[
12x + 24 - 24 = 12x
\]

3. Simplify:

\[
12x = 12x
\]

This equation simplifies to \(12x = 12x\), which is always true.

Since the equation holds for all values of \(x\), we can conclude that there are **infinite solutions**.
Answered by GPT-4o mini
To determine the number of solutions for the equation \(9(x + 1) = 3(5x + 1) - 12\), we will first simplify both sides of the equation.

1. Distribute on both sides:

\[
9x + 9 = 15x + 3 - 12
\]

2. Simplify the right side:

\[
9x + 9 = 15x - 9
\]

3. Next, we will move all terms involving \(x\) to one side and the constant terms to the other side. Let's subtract \(15x\) from both sides:

\[
9x - 15x + 9 = -9
\]

This simplifies to:

\[
-6x + 9 = -9
\]

4. Now, subtract 9 from both sides:

\[
-6x = -9 - 9
\]

This simplifies to:

\[
-6x = -18
\]

5. Finally, divide by \(-6\):

\[
x = 3
\]

We found a single value for \(x\). Therefore, the equation has **one solution**:

\[
\boxed{3}
\]
Answered by GPT-4o mini
The solution to the equation \(9(x + 1) = 3(5x + 1) - 12\) is:

\[
x = 3
\]

This was determined by simplifying the equation step by step, which resulted in a single unique solution.