Question

is 3(x-1)+10=-2x+12 one solution, no solution, or infinitely many solutions?

Answer 1

To determine whether the equation \(3(x - 1) + 10 = -2x + 12\) has one solution, no solution, or infinitely many solutions, we need to simplify and solve the equation.

1. Distribute \(3\) on the left side:
\[
3(x - 1) + 10 = 3x - 3 + 10 = 3x + 7
\]

2. Now, the equation can be rewritten as:
\[
3x + 7 = -2x + 12
\]

3. Next, we want to get all terms involving \(x\) on one side and constant terms on the other side. Add \(2x\) to both sides:
\[
3x + 2x + 7 = 12
\]
This simplifies to:
\[
5x + 7 = 12
\]

4. Now, subtract \(7\) from both sides:
\[
5x = 12 - 7
\]
This simplifies to:
\[
5x = 5
\]

5. Finally, divide both sides by \(5\):
\[
x = 1
\]

Since we found a unique solution \(x = 1\), the equation \(3(x - 1) + 10 = -2x + 12\) has **one solution**.