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:
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Substitute \( t = -1 \) into the expression: \[ 7 + 12|t| = 7 + 12|-1| \]
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Calculate the absolute value: \[ |-1| = 1 \] So the expression becomes: \[ 7 + 12 \cdot 1 \]
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Now, perform the multiplication: \[ 12 \cdot 1 = 12 \]
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Finally, add 7: \[ 7 + 12 = 19 \]
Final Result:
Thus, the value of the expression \( 7 + 12|t| \) when \( t = -1 \) is \[ \boxed{19} \]