Question

Solve the absolute value inequality |0.5x+9|≤−2 .(1 point)
Responses

(−∞,∞)
left parenthesis negative infinity comma infinity right parenthesis

(−∞,−5.5]∪[−3.5,∞)
left parenthesis negative infinity comma negative 5.5 right bracket union left bracket negative 3.5 comma infinity right parenthesis

no solution
no solution

[−14,−22]
left bracket negative 14 comma negative 22 right bracket

Answer 1

To solve the inequality \( |0.5x + 9| \leq -2 \), we need to consider the properties of absolute values.

The expression \( |A| \) (where \( A = 0.5x + 9 \) in this case) is always non-negative, meaning \( |A| \geq 0 \) for any real value of \( A \).

Since the right side of the inequality is \(-2\), which is a negative number, the inequality \( |0.5x + 9| \leq -2 \) has no possible solutions. An absolute value cannot be less than a negative number.

Thus, the answer is:

**no solution**