Solve $|x-1|-2|x+5|>3+x$.
Problem
Source: Kosovo MO 2014 Grade 9, Problem 2
Tags: algebra
07.06.2021 21:38
Not always true. Take $x=1$ for example.
07.06.2021 22:01
ze solution shalt be;
07.06.2021 22:05
There are three cases to this question. First, assume that $x>1.$ Therefore, the equation simplifies to $x-1-2(x+5)>3+x$ which simplifies to $-x-11>3+x.$ This implies that $-7>x$ which leads to no solutions for case one. Second, assume that $-5\leq(x)\leq1.$ Therefore, the equation simplifies to $1-x-2(x+5)>3+x$ which simplifies to $-9-3x>3+x.$ This implies that $-3>x.$ Therefore, the solutions to this case will be $-5\leq(x)<3$ Lastly, assume that $x<-5.$ Therefore, the equation simplifies to $1-x+2(x+5)>3+x$ which simplifies to $x+11>3+x.$ This is true for all x so the solution to this case is $x<-5$ Finally, we add up all the cases to conclude that the final answer is $x<-3$ Hope this helps! Please tell me if there are any errors in my solution.
07.06.2021 22:13
Yup! I have the same thing, this looks good <3