Which equation has no solution?

a. 7v+2=8v-3
b. 3x-5=3x+8-x
c. 4y+5=4y-6
d. 7z+6=-7z-5

the answer is c

To determine which equation has no solution, let's simplify each equation step-by-step:

a. 7v + 2 = 8v - 3
Rearrange the equation: 2 + 3 = 8v - 7v
Combine like terms: 5 = v
This equation has a solution, so it is not the correct answer.

b. 3x - 5 = 3x + 8 - x
Combine like terms: -5 = 8 - x
Rearrange the equation: -5 - 8 = -x
Combine like terms: -13 = -x
Multiply both sides by -1 (to isolate x): 13 = x
This equation has a solution, so it is not the correct answer.

c. 4y + 5 = 4y - 6
Rearrange the equation: 5 = -6
The variable y cancels out on both sides, and we end up with an equation that is not true: 5 = -6. This equation has no solution.

d. 7z + 6 = -7z - 5
Rearrange the equation: 7z + 7z = -5 - 6
Combine like terms: 14z = -11
Simplify: z = -11/14
This equation has a solution, so it is not the correct answer.

Therefore, the equation that has no solution is option c. 4y + 5 = 4y - 6.

To determine which equation has no solution, we need to examine each equation and try to solve it. If we encounter an inconsistency or contradiction, it means that the equation has no solution.

a. 7v + 2 = 8v - 3

To solve this equation, let's transpose the variables to one side and the constants to the other side:

7v - 8v = -3 - 2

Simplifying further:

-v = -5

We can solve for v by multiplying both sides of the equation by -1:

v = 5

Since we found a valid solution, this equation does have a solution.

b. 3x - 5 = 3x + 8 - x

Simplifying the equation:

2x - 5 = 8 - x

Transposing the variables and constants:

2x + x = 8 + 5

3x = 13

Dividing both sides by 3:

x = 13/3

Again, we found a valid solution for x, so this equation does have a solution.

c. 4y + 5 = 4y - 6

Transposing the variables and constants:

4y - 4y = -6 - 5

0 = -11

This equation leads to a contradiction since 0 is not equal to -11. Thus, there is no solution for y in this equation.

d. 7z + 6 = -7z - 5

Transposing the variables and constants:

7z + 7z = - 6 - 5

14z = -11

Dividing both sides by 14:

z = -11/14

Again, we obtained a valid solution for z, so this equation does have a solution.

Therefore, option c. 4y + 5 = 4y - 6 is the equation that has no solution.