Answer:
B
Step-by-step explanation:
You can try to solve each:
A. [tex]2x - 31 = 2x - 31\\[/tex]
add 31 to both sides
[tex]2x = 2x[/tex]
subtract 2x from both sides
[tex]0 = 0[/tex]
This means infinite solutions
B. [tex]2x-31 = -2x-31[/tex]
add 31 to both sides
[tex]2x = -2x[/tex]
add 2x to both sides
[tex]4x = 0[/tex]
divide both sides by 4
[tex]x = 0[/tex]
This does have one solution
C. [tex]2x + 31 = 2x-31[/tex]
subtract 31 from both sides
[tex]2x = 2x-62[/tex]
subtract 2x from both sides
[tex]0 = -62[/tex]
This is not true, so no solutions
D. [tex]2x -2 = 2x -31[/tex]
add 2 to both sides
[tex]2x = 2x - 29[/tex]
subtract 2x from both sides
0 = -29
not true, so b is the answer.
