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Explain Bot To determine which equation has no solution, we can start by simplifying each equation and checking if there is any contradiction or inconsistency.
Let's go through each equation:
1) 7v + 2 = 8v – 3
To simplify this equation, we will gather all the variables on one side and the constants on the other side:
7v - 8v = -3 - 2
-v = -5
Now, we can multiply both sides of the equation by -1 to isolate the variable v:
v = 5
So, this equation does have a solution.
2) 3x – 5 = 3x + 8 – x
Let's simplify this equation as well:
3x - 3x - x = 8 + 5
- x = 13
Multiplying both sides by -1 gives:
x = -13
Therefore, this equation does have a solution.
3) 4y + 5 = 4y – 6
Simplifying:
4y - 4y = -6 - 5
0 = -11
This equation leads to a contradiction (0 ≠ -11). Therefore, this equation has no solution.
4) 7z + 6 = –7z – 5
Simplifying:
7z + 7z = -5 - 6
14z = -11
Dividing both sides by 14, we find:
z = -11/14
Thus, this equation does have a solution.
In conclusion, the equation that has no solution is 4y + 5 = 4y – 6.