Let's fill in the blanks step by step.
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Evaluate the first expression:
- For \( x = -\frac{1}{5} \): \[ 18 - 30x = 18 - 30\left(-\frac{1}{5}\right) \] \[ = 18 + 30 \cdot \frac{1}{5} \] \[ = 18 + 6 \] \[ = 24 \]
Now, fill in the blanks:
- \( 18 - 30(-1/5) = 18 - 6 \)
Therefore, we fill in the first blank: \( 18 - _ = 18 - 6 \)
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Next, evaluate the second expression:
- For \( x = -\frac{1}{5} \): \[ 2(9 - 15x) = 2(9 - 15\left(-\frac{1}{5}\right)) \] \[ = 2(9 + 15 \cdot \frac{1}{5}) \] \[ = 2(9 + 3) \] \[ = 2 \cdot 12 \] \[ = 24 \]
Now to fill the blanks:
- \( 2(9 - 15(-_/5)) = 2(9 - (-3)) \) Since \( 15(-\frac{1}{5}) = -3 \)
Therefore, we fill in the second blank: \( 2(9 - _) = 2(9 - (-3)) \)
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Now we fill the last blank:
- The last expression evaluated: \( 2(_)\) As from the previous calculations \(2(12) \)
In summary, we can fill out:
- \( 18 - 30(-1/5) = 18 - 6 \)
- \( 2(9 - 15(-\frac{1}{5})) = 2(9 - (-3)) \)
- \( 2(12) \)
Now for the final sentence: "Since both of these expressions simplify to the same value for two different values of x, then we know that these two expressions must be equivalent."
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