Question

Can you explain please I don’t understand?

Answer 1

don't be alarmed the two lines just mean absolute value, the problem is asking what is m. the problem is asking what number multipyed by 2, subtracted by 1 will give you 3?

2x2=4 right?

so 4-1=3 there!

m=4

so the problem is 2(4)-1=3

i hope i explained well enough!

Answer 2

|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}.