Question

which of the t-values satisfy the following inequality?
$8 > 3 + \frac{t}{4}$
choose all answers that apply:
a $t = 12$
b $t = 16$
c $t = 20$

Explanation:

Step1: Solve the inequality for \( t \)

Start with the inequality \( 8 > 3 + \frac{t}{4} \). Subtract 3 from both sides:
\( 8 - 3 > \frac{t}{4} \)
\( 5 > \frac{t}{4} \).

Multiply both sides by 4 to isolate \( t \):
\( 5 \times 4 > t \)
\( 20 > t \) or \( t < 20 \).

Step2: Check each option

• Option A (\( t = 12 \)): Since \( 12 < 20 \), \( t = 12 \) satisfies the inequality.
• Option B (\( t = 16 \)): Since \( 16 < 20 \), \( t = 16 \) satisfies the inequality.
• Option C (\( t = 20 \)): Since \( 20 \) is not less than \( 20 \) (it is equal), \( t = 20 \) does not satisfy \( t < 20 \).

Answer:

A. \( t = 12 \), B. \( t = 16 \)