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Simplifying 51 + 6(52v + -85) = -7(-45v + 72) Reorder the terms: 51 + 6(-85 + 52v) = -7(-45v + 72) 51 + (-85 * 6 + 52v * 6) = -7(-45v + 72) 51 + (-510 + 312v) = -7(-45v + 72) Combine like terms: 51 + -510 = -459 -459 + 312v = -7(-45v + 72) Reorder the terms: -459 + 312v = -7(72 + -45v) -459 + 312v = (72 * -7 + -45v * -7) -459 + 312v = (-504 + 315v) Solving -459 + 312v = -504 + 315v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-315v' to each side of the equation. -459 + 312v + -315v = -504 + 315v + -315v Combine like terms: 312v + -315v = -3v -459 + -3v = -504 + 315v + -315v Combine like terms: 315v + -315v = 0 -459 + -3v = -504 + 0 -459 + -3v = -504 Add '459' to each side of the equation. -459 + 459 + -3v = -504 + 459 Combine like terms: -459 + 459 = 0 0 + -3v = -504 + 459 -3v = -504 + 459 Combine like terms: -504 + 459 = -45 -3v = -45 Divide each side by '-3'. v = 15 Simplifying v = 15
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