Question

Decide whether each equation has one solution, no solutions, or infinitely many solutions.
2(x – 3) = 2x,
3(y – 3) = 2y – 9 + y,
10x – 2 – 6x = 3x – 2 + x,
4(x + 3) + 2x = x – 8

Answer 1

thanks

Answer 2

1. 2(x – 3) = 2x
Expanding and simplifying the equation:
2x – 6 = 2x
Subtracting 2x from both sides:
-6 = 0
The equation is contradictory, so it has no solution.

2. 3(y – 3) = 2y – 9 + y
Expanding and simplifying the equation:
3y – 9 = 2y – 9 + y
Combining like terms:
3y – 9 = 3y – 9
Subtracting 3y from both sides:
-9 = -9
The equation is an identity, so it has infinitely many solutions.

3. 10x – 2 – 6x = 3x – 2 + x
Combining like terms:
4x – 2 = 4x – 2
Subtracting 4x from both sides:
-2 = -2
The equation is an identity, so it has infinitely many solutions.

4. 4(x + 3) + 2x = x – 8
Expanding and simplifying the equation:
4x + 12 + 2x = x – 8
Combining like terms:
6x + 12 = x – 8
Subtracting x from both sides:
5x + 12 = -8
Subtracting 12 from both sides:
5x = -20
Dividing both sides by 5:
x = -4
The equation has one solution.

Answer 3

You're welcome! If you have any more questions, feel free to ask.