A community for students.
Here's the question you clicked on:
 0 viewing
mathmath333
 one year ago
solve for \(x\)
mathmath333
 one year ago
solve for \(x\)

This Question is Closed

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align}x6<x^25x+9,\ x\in \mathbb{R}\hspace{.33em}\\~\\ \end{align}}\)

phi
 one year ago
Best ResponseYou've already chosen the best response.2*IF* x>= 6 , you can drop the absolute values, and (try to) solve \[ x  6 < x^2 5x+9 \]

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(6\leq x<+\infty\) , for \(x\geq 6 \) is this correct

phi
 one year ago
Best ResponseYou've already chosen the best response.2in other words, solve \[ x^2 6x+15>0 \] this is a parabola, and you can complete the square to write it as \[ (x3)^2 + 6 >0 \] because (x3)^2 is 0 or more, the left side will always be bigger than 0 but we assumed x>=6, so we can say x>=6 is part of the solution

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(6\leq x<+\infty\) is this correct

phi
 one year ago
Best ResponseYou've already chosen the best response.2yes, that is part of the answer. Now we have to look at the case x<6 then  x  6 can be written as (x6) = x + 6 (if x is less than or equal to 6)

phi
 one year ago
Best ResponseYou've already chosen the best response.2so now we look at \[ x + 6 < x^25x+9\]

phi
 one year ago
Best ResponseYou've already chosen the best response.2or \[ x^2 4x +3 > 0 \] or, factoring \[ (x1)(x3)> 0 \] and assuming \( x \le 6\)

phi
 one year ago
Best ResponseYou've already chosen the best response.2(x1)(x3) is bigger than 0 if it is positive it is positive if both factors are negative (because minus times minus is positive) thus if *both* x1<0 and x3 < 0 or x<1 and at the same time x<3 we will get a positive number. x<1 and x<3 simplifies to x<1 thus x<1 (which is consistent with x<=6, our original assumption) is part of the solution

phi
 one year ago
Best ResponseYou've already chosen the best response.2(x1)(x3) is also positive if both factors are positive. this requires both x>1 and x>3 i..e x>3 thus 3 < x <=6 is part of the solution if we put it together \[ \infty < x < 1 \text{ or } 3 < x < \infty \]

phi
 one year ago
Best ResponseYou've already chosen the best response.2the solution is all real numbers except the closed interval [1,3]

phi
 one year ago
Best ResponseYou've already chosen the best response.2any questions on the steps?
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.