For each linear equation, indicate whether the equation has no solution, one solution. or infinitely many solutions. This problem requires you to show your work. (3 points) Put responses in the correct input to answer the question.
3(x+3)=7+3x+6−x
6x+2−4x=2(x+2)
8(x+2)=5x+16+3x
1) 3(x+3)=7+3x+6−x
Expanding the equation:
3x + 9 = 7 + 9 - x
Combining like terms:
4x + 9 = 16 - x
Bringing like terms to one side:
4x + x = 16 - 9
Solving for x:
5x = 7
Dividing by 5:
x = 7/5
Since the variable x has a unique solution, this equation has one solution.
2) 6x+2−4x=2(x+2)
Simplifying the equation:
2x + 2 = 2x + 4
Subtracting 2x from both sides:
2 = 4
Since this equation simplifies to 2 = 4, which is not true, there is no solution to this equation.
3) 8(x+2)=5x+16+3x
Expanding the equation:
8x + 16 = 5x + 16 + 3x
Combining like terms:
8x + 16 = 8x + 16
Subtracting 8x from both sides:
16 = 16
Since this equation simplifies to 16 = 16, which is true, there are infinitely many solutions to this equation.