Question

which of the following equations have no solutions?
choose all answers that apply:
a $40x + 40 = 40x + 20$
b $-40x + 40 = 20x + 20$
c $20x + 40 = 40x + 20$
d $-20x + 40 = -20x + 20$

Explanation:

Step1: Simplify Equation A

Subtract $40x$ from both sides:
$40x + 40 - 40x = 40x + 20 - 40x$
$40 = 20$

Step2: Simplify Equation B

Add $40x$ to both sides, then subtract 20:
$-40x + 40 + 40x = 20x + 20 + 40x$
$40 = 60x + 20$
$60x = 20$
$x = \frac{1}{3}$

Step3: Simplify Equation C

Subtract $20x$ from both sides, then subtract 20:
$20x + 40 - 20x = 40x + 20 - 20x$
$40 = 20x + 20$
$20x = 20$
$x = 1$

Step4: Simplify Equation D

Add $20x$ to both sides:
$-20x + 40 + 20x = -20x + 20 + 20x$
$40 = 20$

Answer:

A. $40x + 40 = 40x + 20$
D. $-20x + 40 = -20x + 20$