Final answer:
To write the equivalent expression with fewer terms, distribute 1/2 to the terms inside the parentheses, combine like terms, and simplify the constants to get 4t - 12.
Step-by-step explanation:
To write an equivalent expression with fewer terms, we need to simplify the given expression. First, distribute the 1/2 to each term inside the parentheses: 1/2(9 - 4t) = 1/2 * 9 - 1/2 * 4t = 9/2 - 2t. Now, substitute this simplified expression back into the original expression: (2t - 8) - (9/2 - 2t) + 5/2. Next, combine like terms: 2t - 8 - 9/2 + 2t + 5/2. Combine the t terms and constants separately: (2t + 2t) + (-8 - 9/2 + 5/2). Finally, simplify the constants: 4t - 8 - 4. The final equivalent expression with fewer terms is 4t - 12.