Which equation has exactly one solution?
This question requires you to show your work.
(1 point)
Responses
3(x+1)=3x
3 times open paren x plus 1 close paren is equal to 3 x
2x+6=3x+2
2 x plus 6 is equal to 3 x plus 2
9x+3=9x−9
9 x plus 3 is equal to 9 x minus 9
6x+12=6(x+2)
Let's solve each equation and determine how many solutions they have:
1) 3(x+1) = 3x
3x + 3 = 3x
3 = 0
Since 3 does not equal 0, there is no solution to this equation.
2) 2x + 6 = 3x + 2
2x - 3x = 2 - 6
-x = -4
x = 4
This equation has exactly one solution, x = 4.
3) 9x + 3 = 9x - 9
Subtracting 9x from both sides, we get:
3 = -9
Since 3 does not equal -9, there is no solution to this equation.
4) 6x + 12 = 6(x+2)
6x + 12 = 6x + 12
6 = 6
Since 6 equals 6, this equation has infinitely many solutions.
Therefore, the equation with exactly one solution is 2x + 6 = 3x + 2.