evaluate 5 – t/3 when t = 12
The correct answer and explanation is:
Let’s evaluate the expression:
5 – t/3 when t = 12
Step 1: Substitute the value of t into the expression
The original expression is: 5−t35 – \frac{t}{3}
Replace tt with 12: 5−1235 – \frac{12}{3}
Step 2: Simplify the division
Calculate 123\frac{12}{3}: 123=4\frac{12}{3} = 4
Step 3: Subtract
Now subtract 4 from 5: 5−4=15 – 4 = 1
Final answer:
1\boxed{1}
Explanation (300 words):
The given expression is a simple algebraic expression where you substitute a given value for a variable and then perform the arithmetic operations according to the order of operations (PEMDAS/BODMAS).
The expression is 5−t35 – \frac{t}{3}. It involves subtraction and division. When evaluating such expressions, the order of operations states that division must be done before subtraction.
First, we replace the variable tt with the given number 12. This substitution changes the expression from 5−t35 – \frac{t}{3} to 5−1235 – \frac{12}{3}.
Next, perform the division 123\frac{12}{3}. Dividing 12 by 3 equals 4. So now, the expression simplifies to 5−45 – 4.
Finally, we subtract 4 from 5, which gives us 1.
This process highlights an important algebraic skill: substituting variables with numbers and simplifying expressions step-by-step following the correct order of operations. This skill is foundational in algebra and is used across many areas of mathematics and applied sciences.
Understanding how to evaluate expressions with variables allows solving equations, understanding formulas, and interpreting functions. It is critical for problem-solving in fields like physics, engineering, economics, and computer science.
In summary, the evaluation of the expression 5−t35 – \frac{t}{3} for t=12t = 12 results in the value 1 after substituting and simplifying step-by-step correctly.