Question
2. Solve for \( p \). \( -9 p \geq 40.5 \)
Ask by Hampton Sandoval. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( p \leq -\frac{9}{2} \)
Solution
Solve the equation \( -9p \geq 40.5 \).
Solve the inequality by following steps:
- step0: Solve for \(p\):
\(-9p\geq 40.5\)
- step1: Change the signs:
\(9p\leq -40.5\)
- step2: Divide both sides:
\(\frac{9p}{9}\leq \frac{-40.5}{9}\)
- step3: Divide the numbers:
\(p\leq -\frac{9}{2}\)
The solution to the inequality \( -9p \geq 40.5 \) is \( p \leq -\frac{9}{2} \).
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Simplify this solution The Deep Dive
To solve for \( p \), we start with the inequality \( -9p \geq 40.5 \). First, we divide both sides by -9. Remember that when we divide by a negative number, we have to flip the inequality sign. So, we get \( p \leq -\frac{40.5}{9} \). Simplifying that, we find \( p \leq -4.5 \). There you have it, \( p \) is less than or equal to -4.5! Moreover, just to reinforce your understanding, remember that solving inequalities is just like solving equations, with the added twist of flipping that inequality sign when dividing or multiplying by negative numbers. So, keep an eye out for that!
