Sharon has at most $25 to spend on her sister's birthday gift. she already bought a knitting machine for her, which cost $14.99. she would also like to get her sister some skeins of yarn to go with it. each skein costs $2.75.

write an inequality to represent this problem. use y to represent the number of skeins of yarn.
what is the most number of skeins sharon can afford to buy? justify your answer in two or more complete sentences.

the correct answer option is (2x-3)(2x+3).

step-by-step explanation:

we are given the following expression and we are to factorize it:

we are to find such factors that when multiplied they give a result of 36 (9 x 4 = 36) and when added they give a result of 0.

the two such factors of 36 are negative six and postive six.

factorizing the given expression to get:

therefore, the correct factorization of is (2x-3)(2x+3).

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: