Final answer:
To determine which of the following equations has no solution, we need to solve each equation and see if any values for x make the equation true. The equation that has no solution is B. 3x+5-4x =-(x+8).
Step-by-step explanation:
To determine which of the following equations has no solution, we need to solve each equation and see if any values for x make the equation true. If there is no value that satisfies the equation, then it has no solution.
Let's solve each equation:
- A. 4*+4 =7+3x+5: This equation simplifies to 4x = 12 + 3x. Subtracting 3x from both sides gives x = 12, which is a solution. So this equation has a solution.
- B. 3x+5-4x =-(x+8): This equation simplifies to -x + 5 = -x - 8. Adding x to both sides gives 5 = -8, which is not true. So this equation has no solution.
- C. (314x+3) = 2+8x +7+4x: This equation simplifies to 314x + 3 = 2 + 12x + 7. Combining like terms gives 314x + 3 = 12x + 9. Subtracting 12x from both sides gives 302x + 3 = 9, and subtracting 3 from both sides gives 302x = 6. Dividing both sides by 302 gives x = 6/302, which is a solution. So this equation has a solution.
- D. 10x -2(4x+3) +1 = 2x+7-2x: This equation simplifies to 10x - 8x - 6 + 1 = 7. Combining like terms gives 2x - 5 = 7. Adding 5 to both sides gives 2x = 12, and dividing both sides by 2 gives x = 6, which is a solution. So this equation has a solution.
Thus, the equation that has no solution is B. 3x+5-4x =-(x+8).