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The solution for the first inequality is a ≥ 2 or a ∈ [2, ∞), and for the second inequality the solutions are b < -5 or b ∈ (-∞, -5)
<h3>What is inequality?</h3>It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have two inequalities:
a.) -12a +7 ≤31
b.) -9 > 3b +6
a) -12a +7 ≤ 31
-12a ≤ 31 - 7
-12a ≤ 24
-a ≤ 2
a ≥ 2 (sign changed because multiplied by a negative number)
a ∈ [2, ∞)
b.) -9 > 3b +6
-15 > 3b
-5 > b
or
b < -5
b ∈ (-∞, -5)
Thus, the solution for the first inequality is a ≥ 2 or a ∈ [2, ∞), and for the second inequality the solutions are b < -5 or b ∈ (-∞, -5)
Learn more about the inequality here:
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Answer:
Step-by-step explanation:
The parent function is .
We want to transform this function so that its vertex will move from the origin to (3,-6).
In other words, we translate the parent function 3 units to the right and 6 units down,
Let g(x) be the new function then: