Answer: To find the solution set for a in the inequality –3(-x + a) + 7 < 5, we can substitute the given value of x = -12 and solve for a.
Let's substitute x = -12 into the inequality:
–3(-(-12) + a) + 7 < 5
Simplifying further:
–3(12 + a) + 7 < 5
–36 - 3a + 7 < 5
Combining like terms:
–3a - 29 < 5
Now, let's isolate the variable a by moving other terms to the other side of the inequality:
–3a < 5 + 29
–3a < 34
Divide both sides by -3, remembering to reverse the inequality because we are dividing by a negative number:
a > 34 / -3
a > -11.33 (rounded to two decimal places)
Therefore, the solution set for a is a > -11.33.