Inequality solve (x+1)/6<x-(3x-2)/4

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SUMMARY

The inequality solve for the expression (x+1)/6 < x - (3x-2)/4 simplifies to -4 < x. The solution process involves multiplying each term by 12 to eliminate the denominators, resulting in the inequality 2(x+1) < 12x - 3(3x-2). After expanding and combining like terms, the final result is derived by isolating x. The conclusion confirms that the solution is x > -4.

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karush
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Ok a student sent this to me yesterday so want to answer without too many steps

I think the first thing to do is multiply every
term by 12

$2(x+1)<12x-3(3x-2)$
Expanding
$2x+2<12x-9x+6$
 

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That’s fine.
 
skeeter said:
That’s fine.
$\dfrac{x+1}{6}<x-\dfrac{3x-2}{4}$
Expanding
$2x+2<12x-9x+6$
Combine like terms
$2x+2<3x+6$
Subtract 2x from both sides
$2<x+6$
Subtract 6 from both sides
$-4<x$

Hopefully no typos

Looks like answer a.
 
Last edited:

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