Which equation has no solution? (Circle your answer)
7v + 2 = 8v – 3
3x – 5 = 3x + 8 – x
4y + 5 = 4y – 6
7z + 6 = –7z – 5
The equation that has no solution is: 7z + 6 = -7z - 5
The equation that has no solution is 7z + 6 = -7z - 5.
To determine which equation has no solution, we need to solve each equation and see if any of them lead to a contradiction or an inconsistency.
1) 7v + 2 = 8v – 3
To solve this equation, we want to isolate the variable "v" on one side of the equation. Let's subtract 7v from both sides:
7v + 2 - 7v = 8v - 3 - 7v
2 = v - 3
Now, let's add 3 to both sides to isolate "v":
2 + 3 = v - 3 + 3
5 = v
So, the solution to this equation is v = 5. There is a unique solution, so this equation is not the one with no solution.
2) 3x – 5 = 3x + 8 – x
To solve this equation, let's simplify and combine like terms:
3x - 5 = 3x + 8 - x
3x - 5 = 2x + 8
Now, subtract 2x from both sides:
3x - 2x - 5 = 2x - 2x + 8
x - 5 = 8
Finally, add 5 to both sides:
x - 5 + 5 = 8 + 5
x = 13
The solution to this equation is x = 13. There is a unique solution, so this equation is not the one with no solution.
3) 4y + 5 = 4y – 6
To solve this equation, let's simplify and combine like terms:
4y + 5 = 4y - 6
Notice that the variable "y" cancels out on both sides of the equation, leaving us with:
5 = -6
This equation leads to a contradiction. 5 cannot be equal to -6, so this equation has no solution.
4) 7z + 6 = -7z – 5
To solve this equation, let's isolate the variable "z" on one side of the equation by adding 7z to both sides:
7z + 7z + 6 = -7z + 7z – 5
14z + 6 = -5
Now, let's subtract 6 from both sides:
14z + 6 - 6 = -5 - 6
14z = -11
Finally, divide both sides by 14:
14z/14 = -11/14
z = -11/14
The solution to this equation is z = -11/14. There is a unique solution, so this equation is not the one with no solution.
Therefore, the equation with no solution is 4y + 5 = 4y – 6.