Question
Solve the inequality \( \frac{f}{3} \leq \frac{1}{9} \), and write the solution in interval notation
Ask by Reeves Vaughan. in the United States
Feb 27,2025
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Answer
The solution is \( f \leq \frac{1}{3} \), which in interval notation is \( (-\infty, \frac{1}{3}] \).
Solution
Solve the equation \( \frac{f}{3} \leq \frac{1}{9} \).
Solve the inequality by following steps:
- step0: Solve for \(f\):
\(\frac{f}{3}\leq \frac{1}{9}\)
- step1: Multiply both sides:
\(\frac{f}{3}\times 9\leq \frac{1}{9}\times 9\)
- step2: Multiply the terms:
\(3f\leq 1\)
- step3: Divide both sides:
\(\frac{3f}{3}\leq \frac{1}{3}\)
- step4: Divide the numbers:
\(f\leq \frac{1}{3}\)
The solution to the inequality \( \frac{f}{3} \leq \frac{1}{9} \) is \( f \leq \frac{1}{3} \).
In interval notation, the solution is \( (-\infty, \frac{1}{3}] \).
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Simplify this solution Beyond the Answer
To solve the inequality \( \frac{f}{3} \leq \frac{1}{9} \), start by multiplying both sides of the inequality by 3 to eliminate the fraction. This gives us: \[ f \leq \frac{1}{9} \times 3 \] Calculating the right side, we have: \[ f \leq \frac{3}{9} \] Simplifying \( \frac{3}{9} \) yields: \[ f \leq \frac{1}{3} \] In interval notation, the solution is: \[ (-\infty, \frac{1}{3}] \]
