Question

If you are age 12-64, you pay the regular price to attend a movie. Write an absolute equation that has minimum and maximum ages for its solutions.

A. |x - 12| = 64
B. |x - 64| = 12
C. |x - 12| ≤ 64
D. |x - 64| ≥ 12

Answer 1

The correct equation for the regular movie ticket price range for age 12 to 64 is |x - 12| ≤ 64, which includes all ages from 12 up to 76.

Step-by-step explanation:

The correct absolute value equation representing the minimum and maximum ages for paying the regular movie ticket price is |x - 12| ≤ 64. This inequality states that the distance between the age x and 12 must be less than or equal to 64, symbolizing that any age from 12 to 76 is included in the range for paying the regular price (since 12 + 64 = 76).

To verify this, you could consider two cases based on the properties of absolute values:

• Case 1: If x ≥ 12, then x - 12 ≤ 64, which implies x ≤ 76.
• Case 2:strong>: If x < 12, then -(x - 12) ≤ 64, which also leads us to x ≥ 12 after simplifying. Hence, x must be at least 12.

Putting these two cases together, the inequality ensures that the age x must be within or equal to the range of 12 to 76 years old.