46+14w≥138 subtract 46 from both sides
14w≥92 divide both sides by 14
w≥6.57
If we are to assume that she saves the $14 at one time per week, w, weeks must be an integer value, so she won't have saved enough until:
w≥7
So she must save for at least 7 weeks in order to be able to purchase the racket.