GeminiHeat wrote:
a > 4: This is not necessarily true. The given condition a + b < 0 does not provide enough information to determine the value of a.
a < –4: This is not necessarily true. The given condition a + b < 0 does not provide enough information to determine the value of a.
a < –2: This must be true. Since a + b < 0 is given, subtracting b from both sides of the inequality results in a < -b. Substituting a + 2b = 3 into this inequality, we get a < -b < 3. Since a and -b have opposite signs, and a + 2b = 3, which implies 2b > -3, we can deduce that a < -b < 3, which further implies a < -b < 2 < 3. Therefore, a must be less than -2.
2 < a < 4: This is not necessarily true. The given condition a + b < 0 does not provide enough information to determine the value of a.
None of the above: This is not the correct answer, as option 3 (a < -2) must be true based on the given conditions.
Therefore, the correct answer is: a < –2.
Boss, can you please show the steps for how you substituted a+2b in the a<-b eqn ??