Question

Look at the factorization shown below.

0 < –100x² + 350x – 150
0 < –50(2x²– 7x + 3)
0 < –50(2x – 1)(x – 3)
Select the range that Mario can choose from to price his muffins and make a positive profit.
a. x < $0.50
b. $0.50 < x < $3.00
c. $0.50 < x or x > $3.00
d. x > $3.00

Answer 1

To solve the inequality, we find the range of x that makes it true. The possible range for x is x > 0.5 or x < 3.

Step-by-step explanation:

The given inequality is 0 < –50(2x – 1)(x – 3). To solve this inequality, we need to find the range of x that makes the inequality true.

We know that if a product of factors is greater than zero, then either all the factors are greater than zero or exactly one factor is less than zero.

So, for -50(2x - 1)(x - 3) to be greater than zero, either both 2x - 1 and x - 3 should be greater than zero, or exactly one of them should be less than zero.

By setting each factor equal to zero, we find that 2x - 1 = 0 gives x = 1/2 and x - 3 = 0 gives x = 3.

So, the possible range for x is x > 0.5 or x < 3.

Hence, the correct option is c. $0.50 < x or x > $3.00.