Question
Solve the following inequality. Write the solution set in interval notation, and graph it. \( -\frac{4}{5} x<-12 \) The solution set is \( \square \). (Type your answer in interval notation.)
Ask by Kirk Peters. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution set is \( (15, \infty) \).
Solution
Solve the equation \( -\frac{4}{5}x<-12 \).
Solve the inequality by following steps:
- step0: Solve for \(x\):
\(-\frac{4}{5}x<-12\)
- step1: Change the signs:
\(\frac{4}{5}x>12\)
- step2: Multiply by the reciprocal:
\(\frac{4}{5}x\times \frac{5}{4}>12\times \frac{5}{4}\)
- step3: Multiply:
\(x>15\)
The solution to the inequality \( -\frac{4}{5}x < -12 \) is \( x > 15 \).
Therefore, the solution set in interval notation is \( (15, \infty) \).
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Simplify this solution Bonus Knowledge
To solve the inequality \( -\frac{4}{5} x < -12 \), first, multiply both sides by \( -\frac{5}{4} \). Remember, when you multiply or divide by a negative number, you must flip the inequality sign. So, it becomes \( x > 15 \). In interval notation, the solution set is \( (15, \infty) \). Now, if we were to graph this, we would place an open circle at 15 (indicating that 15 is not included in the solution) and shade everything to the right, extending to infinity!
