Question

Which of the following equations has no solution?

A) 4x + 4 = 7 + 3x + 5
B) 3x + 5 - 4x = -(x + 8)
C) 3(4x + 3) = 2 + 8x + 7 + 4x
D) 10x - 2(4x + 3) + 1 = 2x + 7 - 2x

Answer 1

B,C

Look at the x value… cannot be 0

Answer 2

To determine which of the given equations has no solution, simplify each equation and see if you end up with a statement that is not true. The equation that has no solution is B) 3x + 5 - 4x = -(x + 8).

Step-by-step explanation:

To determine which of the given equations has no solution, we need to simplify each equation and see if we end up with a statement that is not true. Let's go through each equation:

1. A) 4x + 4 = 7 + 3x + 5: Start by combining like terms: 4x + 4 = 12 + 3x. Subtract 3x from both sides to isolate the variable: x + 4 = 12. Then, subtract 4 from both sides: x = 8. This equation has a solution of x = 8, so it is not the correct answer.
2. B) 3x + 5 - 4x = -(x + 8): Combine like terms: -x + 5 = -x - 8. Subtract -x from both sides to isolate the variable: 5 = -8. This statement is not true, so this equation has no solution.
3. C) 3(4x + 3) = 2 + 8x + 7 + 4x: Distribute the 3 to the terms inside the parentheses: 12x + 9 = 2 + 8x + 7 + 4x. Combine like terms: 12x + 9 = 15 + 12x. Subtract 12x from both sides to isolate the variable: 9 = 15. This statement is not true, so this equation has no solution.
4. D) 10x - 2(4x + 3) + 1 = 2x + 7 - 2x: Start by simplifying the expression in parentheses: 10x - 8x - 6 + 1 = 2x + 7 - 2x. Combine like terms: 2x - 5 = 5. Subtract 2x from both sides to isolate the variable: -5 = 3. This statement is not true, so this equation has no solution.

Therefore, the correct answer is B) 3x + 5 - 4x = -(x + 8), as it has no solution.