Question

topic: equations and inequalities and absolute value
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
determine the values of k for which the equation has no solutions:
$|2x + 7| - k \leq 5$
$k < 5$
$k > -5$
$k > 5$
$k < -5$

Explanation:

Step1: Rearrange the inequality

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

Step2: Analyze absolute value property

An inequality $|A| \leq B$ has no solutions if $B < 0$, since absolute value is non-negative.

Step3: Solve for k

Set $k + 5 < 0$
$k < -5$

Answer:

D. $k < -5$