To determine which equation has no solution, we need to simplify each option and check for inconsistencies, such as contradictions.
A. \( 8x + 68 - x + 5 = 8x + 6 \)
Simplifying the left side: \[ 8x + 68 - x + 5 = (8x - x) + (68 + 5) = 7x + 73 \]
Setting it equal to the right side: \[ 7x + 73 = 8x + 6 \] Subtract \( 7x \) from both sides: \[ 73 = x + 6 \] Subtract 6 from both sides: \[ x = 67 \] This equation has one solution.
B. \( 3x + 221 - x + 11 = 3x + 2 \)
Simplifying the left side: \[ 3x - x + 221 + 11 = (3x - x) + (221 + 11) = 2x + 232 \]
Setting it equal to the right side: \[ 2x + 232 = 3x + 2 \] Subtract \( 2x \) from both sides: \[ 232 = x + 2 \] Subtract 2 from both sides: \[ x = 230 \] This equation has one solution.
C. \( 4 + 2x8 - 4x = 4 + 2x \)
Assuming this is a typing error and should be \( 4 + 2x - 4x = 4 + 2x \): Simplifying the left side: \[ 4 + 2x - 4x = 4 - 2x \]
Setting it equal to the right side: \[ 4 - 2x = 4 + 2x \] Subtract 4 from both sides: \[ -2x = 2x \] Adding \( 2x \) to both sides: \[ 0 = 4x \] Divide by 4: \[ x = 0 \] This equation has one solution.
D. \( 5x - 5 = 5x - 5 \)
Subtract \( 5x \) from both sides: \[ -5 = -5 \] This is a true statement for all \( x \). This equation has infinitely many solutions.
Since none of these equations (A, B, C) have no solution, reviewing our original assessment, we realize that D does not come as an option indicating no solution.
Thus, none of the equations above have no solution. If these options were intended to refer to a specific context or mistake in setup, please provide further clarification for accurate assessment.