Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Precalculus Mathematics Homework Help
Solve Inequalities algebraically
Reply to thread
Message
[QUOTE="HallsofIvy, post: 4520307, member: 637751"] Since the square root, [itex]\sqrt{2r+ 3}[/itex], is, by definition, nonnegative, you can (almost) ignore it. The product of the two numbers, 3r- 4 and [itex]\sqrt[3]{r- 2}[/itex], will be negative if and only if the two factors are of opposite order. In other words, either 1) 3r- 4> 0 and [itex]\sqrt[3]{r- 2}< 0[/itex] or 2) 3r- 4< 0 and [itex]\sqrt[3]{r- 2}> 0[/itex] Similarly, a positive number, cubed, is positive and a negative number, cubed, is negative. So that can be reduced to 1) 3r- 4> 0 and r- 2< 0 or 2) 3r- 4< 0 and r- 2> 0. 3r- 4> 0 for r> 4/3 and r- 2< 0 for r< 3. Those will both be true for 4/3< r< 3. [itex]\sqrt{2r+ 3}= 0[/itex] only for r= -3/2 and that does not lie between 4/3 and 3. (1) is true for 4/3< r< 3. 3r- r< 0 for r< 4/3 and r- 2> 0 for r> 3. (2) is never true. [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Precalculus Mathematics Homework Help
Solve Inequalities algebraically
Back
Top