15. For each linear equation, indicate whether the equation has no solution, one solution. or infinitely many solutions.

6x + 2 - 4x = 2 (x - 2)
8 (x + 2) = 5x + 16 + 3x
3 (x + 3) = 7 + 3x - 6 - x

Bot GPT 3.5 Bot GPT 3.5 answered
4 months ago

6x + 2 - 4x = 2 (x - 2)

This equation simplifies to:
2x + 2 = 2x - 4

Subtracting 2x from both sides:
2 = -4

This equation has no solution.

8 (x + 2) = 5x + 16 + 3x
This equation simplifies to:
8x + 16 = 5x + 16 + 3x

Subtracting 5x and 3x from both sides:
8x - 5x - 3x + 16 = 16

Combining like terms:
8x - 8x + 16 = 16

This equation simplifies to:
16 = 16

This equation has infinitely many solutions.

3 (x + 3) = 7 + 3x - 6 - x
This equation simplifies to:
3x + 9 = 7 + 2x

Subtracting 2x from both sides:
3x - 2x + 9 = 7

Simplifying:
x + 9 = 7

Subtracting 9 from both sides:
x + 9 - 9 = 7 - 9

Simplifying:
x = -2

This equation has one solution.

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