Question

in 5–8, evaluate each expression for t = 8, w = \frac{1}{2}, and x = 3.\

1. 3t − 8\
2. 6w ÷ x + 9\
3. t² − 12w ÷ x\
4. 5x − 2w + t

Explanation:

Problem 5:

Step1: Substitute \( t = 8 \) into the expression

\( 3t - 8 = 3\times8 - 8 \)

Step2: Calculate the result

First, \( 3\times8 = 24 \), then \( 24 - 8 = 16 \)

Step1: Substitute \( w = \frac{1}{2} \) and \( x = 3 \) into the expression

\( 6w\div x + 9 = 6\times\frac{1}{2}\div3 + 9 \)

Step2: Calculate step by step

First, \( 6\times\frac{1}{2} = 3 \), then \( 3\div3 = 1 \), finally \( 1 + 9 = 10 \)

Step1: Substitute \( t = 8 \), \( w = \frac{1}{2} \), and \( x = 3 \) into the expression

\( t^{2}-12w\div x = 8^{2}-12\times\frac{1}{2}\div3 \)

Step2: Calculate step by step

First, \( 8^{2}=64 \), \( 12\times\frac{1}{2}=6 \), \( 6\div3 = 2 \), then \( 64 - 2 = 62 \)

Answer:

\( 16 \)

Problem 6: