Question

which of the following equations have infinitely many solutions?
choose all answers that apply:
a $-19x - 19 = -19x - 19$
b $-19x + 91 = -19x + 91$
c $-19x - 19 = -19x + 19$
d $-19x - 38 = -19x - 38$

Explanation:

Step1: Analyze Equation A

Add $19x$ to both sides:
$$-19x - 19 + 19x = -19x - 19 + 19x$$
$$-19 = -19$$
This is a true statement, so there are infinitely many solutions.

Step2: Analyze Equation B

Add $19x$ to both sides:
$$-19x + 91 + 19x = -19x + 91 + 19x$$
$$91 = 91$$
This is a true statement, so there are infinitely many solutions.

Step3: Analyze Equation C

Add $19x$ to both sides:
$$-19x - 19 + 19x = -19x + 19 + 19x$$
$$-19 = 19$$
This is a false statement, so there are no solutions.

Step4: Analyze Equation D

Add $19x$ to both sides:
$$-19x - 38 + 19x = -19x - 38 + 19x$$
$$-38 = -38$$
This is a true statement, so there are infinitely many solutions.

Answer:

A. $-19x - 19 = -19x - 19$
B. $-19x + 91 = -19x + 91$
D. $-19x - 38 = -19x - 38$