To find the expression that is equivalent to \((3.1x - 2.4 + 1.9) + (2.2x - 1.4y - 3.4)\), let's simplify it step by step:
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Combine the like terms from both parts of the expression.
\(3.1x + 2.2x\) for the \(x\) terms,
\(-2.4\) and \(1.9\) for the constant terms,
\(-1.4y\) and \(-3.4\) for the \(y\) terms.
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Now let's calculate each part:
- \(3.1x + 2.2x = 5.3x\)
- \(-2.4 + 1.9 = -0.5\)
- \(-1.4y - 3.4 = -1.4y - 3.4\) (we can't combine these since we have different variables)
Putting it all together, we get: \[ 5.3x - 1.4y - 0.5 - 3.4. \]
Now we look at the options given and check if they align with this process:
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For the first option: \((3.1x + 2.2x)+ (-2.4y + 1.4y) +(1.9 + 3.4)\)
- This is incorrect because it adds \(1.9\) and \(3.4\) instead of combining \(-2.4\) and \(1.9\).
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For the second option: \((3.1x + (-2.2x)) + (-2.4 + (-1.4y)) + (1.9 + (-3.4))\)
- This is also incorrect; the \(x\) terms are incorrectly set up.
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For the third option: \((3.1x + 2.2x) + (-2.4 + (-1.4)) + (1.9 + (-3.4))\)
- This sums \(-2.4\) with another term incorrectly.
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For the fourth option: \((3.1x + 2.2x) + (-2.4y + (-3.4)) + (1.9 + (-1.4)\)
- This option incorrectly mixes the signs and variable components.
None of the options provided match the steps we took or lead to the proper simplification.
Thus, the equivalent expression after simplifying \((3.1x - 2.4 + 1.9) + (2.2x - 1.4y - 3.4)\) would be \(5.3x - 1.4y - 0.5\), which matches none of the given options.
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