Question

which of the following equations have no solutions?
choose all answers that apply:
a $-14x + 23 = 14x - 23$
b $14x + 23 = 14x - 23$
c $-23x - 14 = 14x - 23$
d $14x - 23 = 14x - 23$

Explanation:

Step1: Analyze Equation A

Rearrange to isolate $x$:
$-14x - 14x = -23 - 23$
$-28x = -46$
$x = \frac{-46}{-28} = \frac{23}{14}$
This has one solution.

Step2: Analyze Equation B

Cancel $14x$ from both sides:
$23 = -23$
This is a false statement, so no solution.

Step3: Analyze Equation C

Rearrange to isolate $x$:
$-23x -14x = -23 +14$
$-37x = -9$
$x = \frac{-9}{-37} = \frac{9}{37}$
This has one solution.

Step4: Analyze Equation D

Cancel $14x$ from both sides:
$-23 = -23$
This is a true statement, so infinite solutions.

Answer:

B. $14x + 23 = 14x - 23$