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a + 2b = -5

To solve for the value of a + 2b, we first manipulate the equation 6a = -30 - 12b. Dividing the entire equation by 6 gives us a = -5 - 2b, which directly leads to a + 2b = -5.

A) -8

This option is incorrect because substituting -8 into the expression a + 2b does not satisfy the equation derived from 6a = -30 - 12b. If a + 2b equals -8, we would have a different relationship between a and b that contradicts the calculations.

B) -7

Option B is also incorrect. If a + 2b were equal to -7, plugging this into the equation would not yield consistent values for a and b as derived from the original equation. Thus, it cannot be the correct solution.

C) -6

This choice is incorrect as well. Setting a + 2b to -6 does not satisfy the equation obtained from simplifying 6a = -30 - 12b, leading to inconsistencies in the values of a and b.

D) -5

This option is correct. By substituting a = -5 - 2b into the expression a + 2b, we find that it simplifies directly to -5, which confirms it as the valid solution derived from the original equation.

E) -4

This option is incorrect. If a + 2b equaled -4, the relationship derived from the original equation would not hold, leading to a conflict with the established values for a and b.

Conclusion

The value of a + 2b is definitively -5, as calculated from the equation derived from the given expression. All other options do not satisfy the relationship established by the equation 6a = -30 - 12b, confirming that they do not represent the correct solution.