If 6a = -30 - 12b, what is the value of a + 2b?

Rationale

a + 2b = -5.

To solve the equation \(6a = -30 - 12b\) for \(a + 2b\), we can first isolate \(a\) in terms of \(b\) and then substitute it back to find the required expression. Simplifying the equation yields \(a = -5 - 2b\), leading directly to \(a + 2b = -5\).

A (-8) YOUR ANSWER

If \(a + 2b = -8\), substituting back would imply a different relationship than established from the original equation. This choice does not satisfy the equation \(6a = -30 - 12b\) when calculated, yielding inconsistent results.

B (-7) YOUR ANSWER

Choosing \(a + 2b = -7\) would lead to an incorrect substitution in the rearranged equation. The values for \(a\) and \(b\) derived from this choice do not correspond to the original expression of \(6a = -30 - 12b\), indicating this option is not valid.

C (-6) YOUR ANSWER

If \(a + 2b = -6\), it suggests a potential solution; however, substituting these values back into the original equation does not yield consistent results. The derived values for \(a\) and \(b\) do not satisfy the equation \(6a = -30 - 12b\).

D (-5) CORRECT

This answer aligns perfectly with our derived equation, confirming the calculation \(a + 2b = -5\) is accurate. When substituting \(a = -5 - 2b\) back into the original equation, it holds true, verifying that this is indeed the correct solution.

Conclusion

The problem involves manipulating a linear equation to find a specific expression involving \(a\) and \(b\). Through careful algebraic manipulation, we find that \(a + 2b\) equals -5, making option D the only valid choice. The other options fail to satisfy the original equation, confirming that \(a + 2b = -5\) is the definitive solution.

If 6a = -30 - 12b, what is the value of a + 2b?

a + 2b = -5.

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