Answer:
B. 1/13(26x - 169) = 1/12(-156 + 24x)
Explanation:
When looking for an equation with infinetly many solutions, we are looking for an equation that is true when simplified
such as: 3c = 3c
or x - 10 = - 10 + x
this is because any value that we put in for x will simplify to a true equation (will be a solution)
so, let's examine the options:
A. if we combine like-terms on both sides, we will end up with 23 + 32x = 32x + 26
which is false, for any value that we put in for x
B. this statement is true--regardless of the value for x.
1/13 · 26 is the same as 1/12 · 24 (both equal 2; so both sides would distribute to 2x)
1/13th of -169 is -13; and 1/12th of -156 is -13
so, for all values of x, option B is true
(all values of x are a solution; and "x" could be any value)
C. by distributing the 2 (6 - 4x = -5x + 7), we find an equation that is not true for all values of x [we don't even have to find the solution, we just know that there will only be a/a few solution ]
D) because the variable, x, is only on one side (and when distributed, is not cancelled by any other x), we know that it cannot be true for infinetly many solutions
(the only true solution will be when the equation is simplified to 4/18 = 4/18)
hope this helps!!