Question

For what values of x does the binomial 2x−1 take on a positive value?

Answer 1

Part A

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

⇒ 2x - 1 > 0

⇒ 2x > 1

⇒ x > $\frac{1}{2}$

Hence, for all values of x that are greater than $\frac{1}{2}$, 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