Which equation has NO solution?
Responses
A 15x+123
= 5x + 415 x + 12 3 = 5x + 4
B 8−4x10
= 4 + 2x8 − 4 x 10 = 4 + 2x
C 4x−202
= 2x − 104 x − 20 2 = 2x − 10
D 15x+53
= 5x + 6
The equation that has no solution is:
D) 15x + 53 = 5x + 6
To determine which equation has no solution, we need to compare the coefficients and constants on both sides of the equation.
A) 15x + 123 = 5x + 415
B) 8 - 4x * 10 = 4 + 2x
C) 4x - 202 = 2x - 10
D) 15x + 53 = 5x + 6
Let's analyze each equation step-by-step to see if they have solutions:
A) In equation A, we have both x terms on the left side and the constants on the right side. By simplifying the equation, we get 10x + 123 = 415. By subtracting 123 from both sides, we get 10x = 292. And finally, by dividing both sides by 10, we get x = 29.2. Therefore, equation A has a solution (x = 29.2).
B) In equation B, we have terms with both x and constants on both sides. By simplifying the equation, we get -4x * 10 = 4 + 2x. By multiplying -4x and 10, we get -40x = 4 + 2x. By combining like terms on the right side, we get -40x = 2x + 4. By subtracting 2x from both sides, we get -42x = 4. And finally, by dividing both sides by -42, we get x = -4/21. Therefore, equation B has a solution (x = -4/21).
C) In equation C, we again have terms with both x and constants on both sides. By simplifying the equation, we get 4x - 202 = 2x - 10. By subtracting 2x from both sides, we get 2x - 202 = -10. By adding 202 to both sides, we get 2x = 192. And finally, by dividing both sides by 2, we get x = 96. Therefore, equation C has a solution (x = 96).
D) In equation D, we have terms with both x and constants on both sides. By simplifying the equation, we get 15x + 53 = 5x + 6. By subtracting 5x from both sides, we get 10x + 53 = 6. By subtracting 53 from both sides, we get 10x = -47. And finally, by dividing both sides by 10, we get x = -4.7. Therefore, equation D has a solution (x = -4.7).
Based on the above analysis, the equation that has NO solution is B) 8 - 4x * 10 = 4 + 2x.
To determine which equation has no solution, we need to simplify each equation and check if there is a variable on both sides of the equation. If there is, then we will have a solution. However, if there is no variable on one side of the equation, then the equation has no solution.
Let's simplify each equation:
A: 15x + 123 = 5x + 4
Simplifying the equation, we get:
10x + 123 = 4
Since there is a variable (x) on both sides of the equation, this equation has a solution.
B: 8 - 4x * 10 = 4 + 2x
Simplifying the equation, we get:
8 - 40x = 4 + 2x
Since there is a variable (x) on both sides of the equation, this equation has a solution.
C: 4x - 202 = 2x - 10
Simplifying the equation, we get:
2x - 202 = -10
Again, there is a variable (x) on both sides of the equation, so this equation has a solution.
D: 15x + 53 = 5x + 6
Simplifying the equation, we get:
10x + 53 = 6
Once again, there is a variable (x) on both sides of the equation, so this equation has a solution.
Therefore, none of the given equations have no solution.