Question

Determine the values of k for which the equation has no solution

Answer 1

To solve this, we would need to figure out the values of $k$ 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,

$|2x+7|\leq 5+k$

So $5+k$ cannot be negative. So,

$5+k\geq 0\\k\geq -5$

For this to have a solution, k needs to be greater than or equal to $-5$.

For no solution, k is less than -5. So, values of k which will make the equation to not have any solution is $k$.

ANSWER:  $k$