To simplify the expression \((3.1x - 2.4 + 1.9) + (2.2x - 1.4y - 3.4)\), we can break it down as follows:
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First, group the similar terms from both groups of the expression:
- Combine the \(x\) terms: \(3.1x + 2.2x\)
- Combine the constant terms: \(-2.4 + 1.9 - 3.4\)
- Combine the \(y\) term: \(-1.4y\)
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Now, we will simplify each group:
- For the \(x\) terms: \[ 3.1x + 2.2x = 5.3x \]
- For the constant terms: \[ -2.4 + 1.9 - 3.4 = -4.9 \]
- For the \(y\) term, it remains \(-1.4y\).
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Putting these simplified terms together, we have: \[ 5.3x - 1.4y - 4.9 \]
Now, comparing this simplified expression with the answer options provided:
- \((3.1x + 2.2x) + (-2.4y + 1.4y) + (1.9 + (-3.4))\)
- \((3.1x + (-2.2x)) + (-2.4 + (-1.4y)) + (1.9 + (-3.4))\)
- \((3.1x + 2.2x) + (-2.4 + (-1.4)) + (1.9 + (-3.4))\)
- \((3.1x + 2.2x) + (-2.4y + (-3.4)) + (1.9 + (-1.4))\)
The first choice contains \(-2.4y\), which is incorrect since we only have \(-1.4y\).
The second choice has \((-2.2x)\) instead of the combined \(x\) terms, so it is not valid either.
The third choice has a combination of \(-2.4\), which doesn't correctly represent the constant terms since it doesn't sum them correctly.
The fourth choice, \((3.1x + 2.2x) + (-2.4y + (-3.4)) + (1.9 + (-1.4))\), also does not match due to incorrect combinations of the variables and constants.
None of these options provide the correct equivalent expression, but reconstructing the original expression correctly suggests that the simplified expression should emphasize positive constants and variable terms correctly.
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