For what values of x does the binomial 2x−1 take on a positive value? for what values of y does the binomial 21−3y take on a negative value? for what values of c does the binomial 5−3c take on a value which is greater than 80?

Part A

We need to determine values of x for which 2x−1 is positive

⇒ 2x - 1 > 0

⇒ 2x > 1

⇒ x >

Hence, for all values of x that are greater than , the binomial 2x-1 is positive

Part B

We need to determine values of y for which 21−37 is negative

⇒ 21-3y < 0

⇒ 21 < 3y

⇒ 7 < y

Hence, for all values of y that are greater than 7, the binomial 21-37 is negative

Part C

We need to determine values of c for which 5−3c is greater than 80

⇒ 5-3c > 80

⇒ -3c > 75

⇒ -c > 25

⇒ c < -25

Hence, for all values of c that are less than -25, the binomial 5-3c is greater than 80

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.