1/x < 4 solve the inequality
in Algebra 1 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

1/x<4. Multiply through by x: 1<4x, assuming x>0.

Divide through by 4: ¼<x, so x>¼, which is positive as assumed.

If x<0, then multiplying through by x reverses the inequality: 1>4x, ¼>x, x<¼, but this creates a contradiction because x can be less than ¼ but greater than zero, violating the condition x<0. Also x≠0. To resolve the contradiction, x<0.

Conclusion: x<0 or x>¼.

Check: Let x=½, then 1/x=2<4, so the inequality holds. Let x=1, then 1<4 and the inequality holds.

Let x=-¼, 1/x=-4<4 and the inequality holds. Let x=-1, -1<4 and the inequality holds.

by Top Rated User (737k points)

No related questions found

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
84,769 questions
89,821 answers
2,031 comments
29,938 users