Question

Which of the following equations have infinitely many solutions?

Choose all answers that apply:
46x - 23 = 46x + 23
-46x + 23 = 46x + 23
46x + 23 = 46x +23
-46x - 23 = 46x + 23

Answer 1

46x + 23 = 46x +23

Explanation:

46x - 23 = 46x + 23

Subtract 46x from each side

-23 = 23

This is not true so there are no solutions

-46x + 23 = 46x + 23

Add 46x to each side

23 = 96x +23

Subtract 23 from each side

0 = 96x

x=0 one solution

46x + 23 = 46x +23

Subtract 46x from each side

23 = 23

This is always true so there are infinite solutions

-46x - 23 = 46x + 23

add 46x to each side

-23 = 96x +23

subtract 23 from each side

-46 = 96x

x = -1/2