Answer:
when it simplifies to 0=0
Step-by-step explanation:
An equation has "all real numbers" as its solution when it can be simplified to ...
0 = 0 . . . has "all real numbers" as a solution set
__
Example:
3x +6 = 2x +10 +x -4
Subtract (3x+6) from both sides:
(3x +6) -(3x +6) = (2x +10 +x -4) -(3x +6)
0 = x(2 +1 -3) +(10 -4 -6)
0 = 0x +0
0 = 0 . . . . has "all real numbers" as a solution set (True for every value of x.)
Example 2:
6x +2 -2x = 4x +1
Subtract (4x+1) from both sides:
(6x +2 -2x) -(4x +1) = (4x +1) -(4x +1)
x(6 -2 -4) +(2 -1) = 0
0x +1 = 0
1 = 0 . . . . . does not have "all real numbers" as a solution set. There is no solution. (No value of x will make this true.)
