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Evaluate the expression for t = –1.

7 + 12|t| =
question

key idea

solution

1 answer

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 \[ \boxed{19} \]