Which of the following values for b makes the inequality −32.5−6b≥48.5 true? Responses −13 negative 13 −12.5 negative 12.5 −12 negative 12 −13.5 negative 13.5
The inequality is: -32.5 - 6b ≥ 48.5.
To make this inequality true, we need to find a value for b that satisfies the inequality.
Adding 32.5 to both sides, we have: -6b ≥ 81.
Now, divide both sides by -6 (note that when dividing/multiplying an inequality by a negative number, we need to flip the inequality sign):
b ≤ -81/6 = -13.5.
Thus, the correct answer is negative 13.5.
To find the possible values for b that make the inequality −32.5−6b ≥ 48.5 true, we need to solve the inequality for b.
First, let's add 32.5 to both sides of the inequality to isolate the variable term:
−32.5 − 6b + 32.5 ≥ 48.5 + 32.5
This simplifies to:
−6b ≥ 81
Next, we divide both sides of the inequality by -6. Considering that we are dividing by a negative number, we need to flip the inequality sign:
b ≤ 81/(-6)
Simplifying the right side:
b ≤ -13.5
Therefore, the value of b that makes the inequality true is any value less than or equal to -13.5.
In the given options, the correct response would be "−13.5 negative 13.5".
To find the values of b that make the inequality −32.5−6b≥48.5 true, we need to solve the inequality. Let's go step by step:
1. Start with the given inequality: −32.5−6b≥48.5.
2. Add 32.5 to both sides of the inequality to isolate the term containing b:
−32.5 + 32.5 − 6b ≥ 48.5 + 32.5
-6b ≥ 81
3. Divide both sides of the inequality by -6. Since we are dividing by a negative number, we need to reverse the inequality sign:
b ≤ 81 / (-6)
b ≤ -13.5
Therefore, the values for b that make the inequality true are b ≤ -13.5.
Out of the given responses, the correct answer is:
-13.5 (negative 13.5)