Consider this relation: A

Question

is equal to the sum of two times B
and 19. Which of the following options models the inverse of the relation?(1 point)
Responses

B=A−192
upper B equals Start Fraction upper A minus 19 over 2 End Fraction

B=A+192
upper B equals Start Fraction upper A plus 19 over 2 End Fraction

B=2A+19
upper B equals 2 upper A plus 19

B=2A−19

Answer 1

To find the inverse of the relation given, we first express the original relation mathematically. The relation states:

\[ A = 2B + 19 \]

Now, we want to express \( B \) in terms of \( A \) (the inverse).

1. Start with the original equation: \[ A = 2B + 19 \]

2. Subtract 19 from both sides: \[ A - 19 = 2B \]

3. Divide both sides by 2 to solve for \( B \): \[ B = \frac{A - 19}{2} \]

This means the inverse of the relation is:

\[ B = \frac{A - 19}{2} \]

From the options provided, the correct model that represents the inverse of the relation is:

Upper B equals Start Fraction upper A minus 19 over 2 End Fraction (which is the same as \( B = \frac{A - 19}{2} \)).