Question

select the correct answer. given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24? a. {-12, -4, 6} b. {-4, 4, 14} c. {2, 4, 9} d. {12, 4, -6}

Explanation:

Step1: Solve the equation for y

First, we need to express \( y \) in terms of \( x \) from the equation \( 12x + 6y = 24 \).
Subtract \( 12x \) from both sides: \( 6y = 24 - 12x \)
Divide both sides by 6: \( y=\frac{24 - 12x}{6}=4 - 2x \)

Step2: Find y for x = -4

Substitute \( x=-4 \) into \( y = 4-2x \):
\( y = 4-2\times(-4)=4 + 8 = 12 \)

Step3: Find y for x = 0

Substitute \( x = 0 \) into \( y = 4-2x \):
\( y = 4-2\times0 = 4 \)

Step4: Find y for x = 5

Substitute \( x = 5 \) into \( y = 4-2x \):
\( y = 4-2\times5 = 4-10=-6 \)

Answer:

D. {12, 4, -6}