Question

which of the following is a solution to the inequality below?
\\(\frac{w}{20} leq -6\\)
\\(w = 80\\)
\\(w = 60\\)
\\(w = -120\\)
\\(w = 100\\)

Explanation:

Step1: Solve the inequality for \( w \)

To solve \( \frac{w}{20} \leq -6 \), we multiply both sides of the inequality by 20. Since 20 is a positive number, the direction of the inequality sign remains the same.
\[
\frac{w}{20} \times 20 \leq -6 \times 20
\]
\[
w \leq -120
\]

Step2: Check each option

• For \( w = 80 \): \( 80 \leq -120 \) is false.
• For \( w = 60 \): \( 60 \leq -120 \) is false.
• For \( w = -120 \): \( -120 \leq -120 \) is true (because the inequality is "less than or equal to").
• For \( w = 100 \): \( 100 \leq -120 \) is false.

Answer:

\( w = -120 \)