To determine which of the given values for \( b \) satisfies the inequality \( -32.5 - 6b \geq 48.5 \), we first need to solve the inequality for \( b \).
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Start by isolating the term with \( b \): \[ -6b \geq 48.5 + 32.5 \] \[ -6b \geq 81 \]
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Next, divide both sides by -6. Remember that when you divide or multiply both sides of an inequality by a negative number, the direction of the inequality changes: \[ b \leq -\frac{81}{6} \] \[ b \leq -13.5 \]
Now we can evaluate the given values of \( b \):
- \( -12.5 \): \( -12.5 \) is greater than \( -13.5 \) (not valid)
- \( -13 \): \( -13 \) is greater than \( -13.5 \) (not valid)
- \( -12 \): \( -12 \) is greater than \( -13.5 \) (not valid)
- \( -13.5 \): \( -13.5 \) is equal to \( -13.5 \) (valid)
The only value that satisfies the inequality \( b \leq -13.5 \) is \( -13.5 \).
So the answer is: −13.5
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