To solve this, we would need to figure out the values of [tex]k[/tex] for which an absolute value is negative. From basics, you should know that an absolute value is always greater than or equal to 0.
If we rearrange this equation a little bit, we get,
[tex]|2x+7|\leq 5+k[/tex]
So [tex]5+k[/tex] cannot be negative. So,
[tex]5+k\geq 0\\k\geq -5[/tex]
For this to have a solution, k needs to be greater than or equal to [tex]-5[/tex].
For no solution, k is less than -5. So, values of k which will make the equation to not have any solution is [tex]k<-5[/tex].
ANSWER: [tex]k<-5[/tex]
