Which of the following values for b makes the inequality -32.5 - 6b _> 48.5 true?
To determine which values for b make the inequality -32.5 - 6b ≥ 48.5 true, we can solve the inequality for b.
Starting with:
-32.5 - 6b ≥ 48.5
Add 32.5 to both sides of the inequality:
-6b ≥ 81
Now, divide both sides of the inequality by -6. Since we are dividing by a negative number, we must reverse the inequality sign:
b ≤ -81/6
Simplifying the right side:
b ≤ -13.5
Therefore, any value of b less than or equal to -13.5 will make the inequality true.
To solve the inequality -32.5 - 6b ≥ 48.5, we need to isolate the variable b.
Step 1: Start by subtracting -32.5 from both sides of the inequality:
-32.5 - 6b - (-32.5) ≥ 48.5 - (-32.5)
Simplifying:
-6b ≥ 81
Step 2: Divide both sides of the inequality by -6. However, when dividing an inequality by a negative number, we need to reverse the inequality sign.
-6b/(-6) ≤ 81/(-6)
Simplifying:
b ≤ -13.5
Therefore, any value of b that is less than or equal to -13.5 will make the inequality -32.5 - 6b ≥ 48.5 true.
To find the values of b that make the inequality -32.5 - 6b ≥ 48.5 true, we need to solve the inequality.
Step 1: Add 32.5 to both sides of the inequality:
-32.5 - 6b + 32.5 ≥ 48.5 + 32.5
-6b ≥ 81
Step 2: Divide both sides of the inequality by -6. Since we are dividing by a negative number, the inequality symbol will flip.
(-6b) / (-6) ≤ 81 / (-6)
b ≤ -13.5
Therefore, the values of b that make the inequality true are b ≤ -13.5.