Question

which of the following is the solution to $|x| + 5 \leq 1$? \
\
a. all values are solutions \
b. no solution \
c. $x \leq -4$ and $x \geq -6$ \
d. $x \leq -4$

Explanation:

Step1: Isolate the absolute value

Subtract 5 from both sides of the inequality \(|x| + 5 \leq 1\).
\[|x| + 5 - 5 \leq 1 - 5\]
\[|x| \leq -4\]

Step2: Analyze the absolute value inequality

The absolute value of a number \(|x|\) is always non - negative (i.e., \(|x| \geq 0\) for all real numbers \(x\)). But we have \(|x| \leq - 4\), and a non - negative number cannot be less than or equal to a negative number. So, there are no real numbers \(x\) that satisfy the inequality \(|x|+5\leq1\).

Answer:

B. No solution