Question

Evaluate the expression for t = –1.

7 + 12|t| =
question


key idea


solution

Answer 1

To evaluate the expression \( 7 + 12|t| \) for \( t = -1 \), follow these steps:

### Key Idea:
When evaluating an expression with an absolute value, remember that the absolute value \( |t| \) is always non-negative. For negative values of \( t \), the absolute value converts it to a positive value.

### Solution:
1. Substitute \( t = -1 \) into the expression:
\[
7 + 12|t| = 7 + 12|-1|
\]

2. Calculate the absolute value:
\[
|-1| = 1
\]
So the expression becomes:
\[
7 + 12 \cdot 1
\]

3. Now, perform the multiplication:
\[
12 \cdot 1 = 12
\]

4. Finally, add 7:
\[
7 + 12 = 19
\]

### Final Result:
Thus, the value of the expression \( 7 + 12|t| \) when \( t = -1 \) is
\[
\boxed{19}
\]