No solutions, one solution, or infinitely many solutions???
2(x – 3) = 2x
No solution*
one solution
infinitely solution
3(y – 3) = 2y – 9 + y
No solution
one solution
infinitely solution
10x – 2 – 6x = 3x – 2 + x
No solution
one solution
infinitely solution
4(x + 3) + 2x = x – 8
No solution
one solution
infinitely solution
the last has a solution
4x+12+2x=x-8
7x=-20
x=-20/7
the third
combining each side
4x-2=4x-2
all x (infinite solution)
the second
3(y – 3) = 2y – 9 + y
3y-9=3y-9
all y (infinite solution)
the first:
2(x – 3) = 2x
2x-6=2x
no solution
thank you bobpursley for the 100%
To determine whether the given equations have no solution, one solution, or infinitely many solutions, we need to solve the equations and observe the resulting solutions.
1) 2(x - 3) = 2x
To simplify the equation, we can distribute the 2 on the left side:
2x - 6 = 2x
Notice that the variable "x" appears on both sides of the equation. If we subtract 2x from both sides, we get:
-6 = 0
Since -6 is not equal to 0, we can conclude that there is no solution for this equation. Therefore, the correct answer is "No solution."
2) 3(y - 3) = 2y - 9 + y
Once again, we can simplify the equation by distributing the 3 on the left side:
3y - 9 = 2y - 9 + y
Combining like terms, we have:
3y - 9 = 3y - 9
This equation has the same variable on both sides. If we subtract 3y from both sides, we get:
-9 = -9
Since -9 is indeed equal to -9, the equation holds true for any value of y. Therefore, there are infinitely many solutions for this equation.
3) 10x - 2 - 6x = 3x - 2 + x
Let's simplify the equation by combining like terms:
4x - 2 = 4x - 2
Similar to the previous case, we have the same variable on both sides. If we subtract 4x from both sides, we get:
-2 = -2
Since -2 is equal to -2, this equation holds true for any value of x. Therefore, there are infinitely many solutions.
4) 4(x + 3) + 2x = x - 8
Expanding and simplifying the equation, we get:
4x + 12 + 2x = x - 8
Combining like terms, we have:
6x + 12 = x - 8
If we subtract x from both sides and simplify further, we get:
5x + 12 = -8
Subtracting 12 from both sides, we have:
5x = -20
Dividing both sides by 5, we get:
x = -4
Thus, we have found a specific value for x. Therefore, there is one solution for this equation.
In summary:
1) 2(x - 3) = 2x has no solution.
2) 3(y - 3) = 2y - 9 + y has infinitely many solutions.
3) 10x - 2 - 6x = 3x - 2 + x has infinitely many solutions.
4) 4(x + 3) + 2x = x - 8 has one solution.