Question

for each value of w, determine whether it is a solution to 49 ≤ 37 + w. (a) is w = 14 a solution? yes no (b) is w = 16 a solution? yes no (c) is w = 8 a solution? yes no (d) is w = 12 a solution? yes no

Explanation:

Step1: Solve the inequality for w

To determine if a value of \( w \) is a solution to \( 49 \leq 37 + w \), we first solve the inequality for \( w \). Subtract 37 from both sides:
\( 49 - 37 \leq w \)
\( 12 \leq w \) or \( w \geq 12 \).

Step2: Check each value

(a) \( w = 14 \)

Since \( 14 \geq 12 \), \( w = 14 \) satisfies \( w \geq 12 \). So it is a solution.

(b) \( w = 16 \)

Since \( 16 \geq 12 \), \( w = 16 \) satisfies \( w \geq 12 \). So it is a solution.

(c) \( w = 8 \)

Since \( 8 < 12 \), \( w = 8 \) does not satisfy \( w \geq 12 \). So it is not a solution.

(d) \( w = 12 \)

Since \( 12 \geq 12 \) (equality holds), \( w = 12 \) satisfies \( w \geq 12 \). So it is a solution.

Answer:

(a) Yes
(b) Yes
(c) No
(d) Yes