Question

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

Explanation:

Step1: Solve the equation for y

Start with the equation \(12x + 6y = 24\). First, isolate \(y\) by subtracting \(12x\) from both sides: \(6y = 24 - 12x\). Then divide every term by 6: \(y=\frac{24 - 12x}{6}=4 - 2x\).

Step2: Substitute \(x = - 4\)

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

Step3: Substitute \(x = 0\)

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

Step4: Substitute \(x = 5\)

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

Answer:

B. \(\{12, 4, - 6\}\)