Question
Question Solve the inequality \( -14 z<-37 \), and write the solution in interval notation.
Ask by Lindsey Delgado. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \( z > \frac{37}{14} \) or in interval notation, \( \left( \frac{37}{14}, \infty \right) \).
Solution
To solve the inequality -14z < -37, follow these steps:
1. Divide both sides by -14. Remember that dividing by a negative number reverses the inequality sign.
z > (-37)/(-14)
2. Simplify the fraction:
z > 37/14
This means z must be greater than 37/14.
In interval notation, the solution is:
(37/14, ∞)
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Simplify this solution Bonus Knowledge
To solve the inequality \( -14 z < -37 \), start by dividing both sides by \( -14 \). Remember that when dividing or multiplying an inequality by a negative number, you need to reverse the inequality sign. Thus, the inequality becomes \( z > \frac{-37}{-14} \), which simplifies to \( z > \frac{37}{14} \) or \( z > 2.64 \). In interval notation, the solution is written as \( (2.64, \infty) \). So any value of \( z \) greater than approximately 2.64 will satisfy the inequality!
