Can you explain i don’t understand?

|2m-1| = 3 is an absolute value equation and as such translates into two separate, different equations.  Just suppose that the quantity 2m-1 is already positive; then the absolute value operator has no effect on 2m-1.  Thus, in this first case,

2m - 1 = 3, or 2m = 4, or m = 2.  This is one of the two solutions of this absolute value equation.

The other case is where the quantity 2m-1 is negative.  Applying the absolute value operator to this results in -(2m-1), or -2m+1.  We then write -2m+1=3.  Subtracting 1 from both sides of this eqn results in -2m= 2, or m= -1.  This is the 2nd solution of the absolute value equation.

Thus, your solution set is {-1, 2}.

step-by-step explanation:

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