Question

Which equation has NO solution?
Responses
A




= 8x + 68 x + 5 2 = 8x + 6
B




= 3x + 221 x + 11 7 = 3x + 2
C




= 4 + 2x8 − 4 x 10 = 4 + 2x
D




= 5x − 5

Answer 1

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.**

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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.