Let's fill in the blanks step-by-step while simplifying the expression \((6.8 - 2x) - (4.1x + 3) + (x - 1.5)\).
Starting with the first line:
- Distributing the negative: \[ (6.8 - 2x) - (4.1x + 3) + (x - 1.5) \implies 6.8 - 2x - 4.1x - 3 + x - 1.5 \] Therefore, \[ 6.8 - 2x - 4.1x - \mathbf{3} + x - \mathbf{1.5} \]
Next, let's combine like terms:
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Combining the x terms: \[ -2x - 4.1x + x \] This gives: \[ -2 - 4.1 + 1 \]
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Combining the constant terms: \[ 6.8 - 3 - 1.5 \] This results in: \[ = 2.3 \]
Putting these two simplifications together in 4.: \[ x (-2 - 4.1 + 1) + \mathbf{2.3} \] So, filling in the blanks:
- For the second blank: 3
- For the third blank (constant): 2.3
Ultimately, we can summarize the final expression: \[ = -5.1x + 2.3 \]
Thus, the filled format should look like:
6.8 - 2x - 4.1x - 3 + x - 1.5
-2x - 4.1x + x + 6.8 - 3 - 1.5
x (-2 - 4.1 + 1) + 2.3
= -5.1x + 2.3
So, the completed sentences would be:
- The second blank is 3.
- The third blank is 2.3.
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