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Which equation is equivalent to \( 4 x+3+(-3 x)+7 x-6 x=11 \) ? A. \( 8 x+3=11 \) B. \( 2 x+3=11 \) C. \( 5 x=11 \) D. \( -4 x=11 \)

Ask by Clarke Bowen. in the United States
Feb 25,2025

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Tutor-Verified Answer

Answer

The equivalent equation is \( 2x + 3 = 11 \), which is option B.

Solution

Let's simplify the left-hand side of the equation step by step: 1. Combine the x-terms:   4x + (-3x) = x,   x + 7x = 8x,   8x - 6x = 2x. 2. The constant term remains:   +3. So, the equation simplifies to:   2x + 3 = 11. Therefore, the equivalent equation is option B: 2x + 3 = 11.

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Mind Expander

Let's simplify the left side of the equation step by step! First, we combine like terms: \(4x\), \(-3x\), and \(7x\) gives us \(4x - 3x + 7x = 8x\). Next, we simplify the constants: \(3 - 6\) results in \(-3\). So, we have \(8x - 3 = 11\). Now, to isolate \(8x\), we can add \(3\) to both sides, resulting in \(8x = 11 + 3\), which simplifies to \(8x = 14\). However, none of the given options directly match this, so let's see which rearrangement could be equivalent after further simplification. If you still want to test the options given: A. \(8x + 3 = 11\) (this is the set-up step we started with). B. Rewrite: \(2x + 3 = 11\) would imply \(x = 4\) which doesn't come from our simplified raw. C. \(5x = 11\) doesn't relate to our total either. D. It's close! If we isolated variables correctly it's just \(8x = 14\) but we see options are flipped. Ultimately, correct re-checks show logical miswriting, leading to -3 being possible missing from further chance of options. The key takeaway here is the importance of combining like terms carefully!

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Algebra Mexico Feb 26, 2025
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