Which equation has no solution?
(1 point)
Responses
5v + 3 = 5v – 5
2x – 4 = 2x + 7 – x
2y + 5 – y = 2y – 3(y – 6)
7z + 9 = –7z – 6
The equation that has no solution is:
2x – 4 = 2x + 7 – x
Solve the following equation.
3(x – 7) – x = 2x – 21
(1 point)
Let's solve the equation step by step:
3(x - 7) - x = 2x - 21
First, distribute the 3:
3x - 21 - x = 2x - 21
Combine like terms:
2x - 21 = 2x - 21
Subtract 2x from both sides:
-21 = -21
The equation simplifies to -21 = -21, which is true for any value of x. Therefore, this equation has infinitely many solutions.
To determine which equation has no solution, we need to simplify each equation and check if the variable cancels out, resulting in a true statement or a false statement. Let's evaluate each equation step-by-step:
1) 5v + 3 = 5v - 5
Simplifying both sides, we get:
5v + 3 ≠ 5v - 5
By subtracting 5v from both sides, we get:
3 ≠ -5
This equation is false, meaning it has no solution.
2) 2x - 4 = 2x + 7 - x
Simplifying both sides, we get:
2x - 4 ≠ x + 7
By subtracting 2x from both sides, we get:
-4 ≠ x + 7 - 2x
-4 ≠ -x + 7
By subtracting 7 from both sides, we get:
-11 ≠ -x
To isolate x, we multiply both sides by -1:
11 = x
This equation is true, meaning it does have a solution.
3) 2y + 5 - y = 2y - 3(y - 6)
Simplifying both sides, we get:
y + 5 = 2y - 3y + 18
Combining like terms, we get:
y + 5 = -y + 18
Adding y to both sides, we get:
2y + 5 = 18
By subtracting 5 from both sides, we get:
2y = 13
Dividing both sides by 2, we get:
y = 6.5
This equation is true, meaning it does have a solution.
4) 7z + 9 = -7z - 6
Simplifying both sides, we get:
7z + 9 ≠ -7z - 6
By adding 7z to both sides, we get:
14z + 9 ≠ -6
By subtracting 9 from both sides, we get:
14z ≠ -15
To isolate z, we divide both sides by 14:
z ≠ -15/14
This equation is true, meaning it does have a solution.
In conclusion, the equation that has no solution is: 5v + 3 = 5v - 5.
To determine which equation has no solution, we need to solve each equation and see if we arrive at a valid solution or if there is a contradiction.
Let's analyze each equation step by step:
1. 5v + 3 = 5v – 5
Subtracting 5v from both sides, we get:
3 = -5
This equation has no solution because it results in two different values.
2. 2x – 4 = 2x + 7 – x
Combining like terms, we have:
2x - 4 = x + 7
Subtracting x from both sides, we get:
x - 4 = 7
Adding 4 to both sides, we have:
x = 11
This equation has a solution, x = 11.
3. 2y + 5 – y = 2y – 3(y – 6)
Distributing the negative sign inside the parentheses, we get:
2y + 5 - y = 2y - 3y + 18
Combining like terms, we have:
y + 5 = -y + 18
Adding y to both sides, we get:
2y + 5 = 18
Subtracting 5 from both sides, we have:
2y = 13
Dividing both sides by 2, we get:
y = 6.5
This equation has a solution, y = 6.5.
4. 7z + 9 = –7z – 6
Adding 7z to both sides, we get:
14z + 9 = -6
Subtracting 9 from both sides, we have:
14z = -15
Dividing both sides by 14, we get:
z = -15/14
This equation has a solution, z = -15/14.
Based on our analysis, the equation that has no solution is 5v + 3 = 5v – 5.