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Simplifying 3(4v + 1) + -3(2v + 3) = 2(v + -7) + 4v + 8 Reorder the terms: 3(1 + 4v) + -3(2v + 3) = 2(v + -7) + 4v + 8 (1 * 3 + 4v * 3) + -3(2v + 3) = 2(v + -7) + 4v + 8 (3 + 12v) + -3(2v + 3) = 2(v + -7) + 4v + 8 Reorder the terms: 3 + 12v + -3(3 + 2v) = 2(v + -7) + 4v + 8 3 + 12v + (3 * -3 + 2v * -3) = 2(v + -7) + 4v + 8 3 + 12v + (-9 + -6v) = 2(v + -7) + 4v + 8 Reorder the terms: 3 + -9 + 12v + -6v = 2(v + -7) + 4v + 8 Combine like terms: 3 + -9 = -6 -6 + 12v + -6v = 2(v + -7) + 4v + 8 Combine like terms: 12v + -6v = 6v -6 + 6v = 2(v + -7) + 4v + 8 Reorder the terms: -6 + 6v = 2(-7 + v) + 4v + 8 -6 + 6v = (-7 * 2 + v * 2) + 4v + 8 -6 + 6v = (-14 + 2v) + 4v + 8 Reorder the terms: -6 + 6v = -14 + 8 + 2v + 4v Combine like terms: -14 + 8 = -6 -6 + 6v = -6 + 2v + 4v Combine like terms: 2v + 4v = 6v -6 + 6v = -6 + 6v Add '6' to each side of the equation. -6 + 6 + 6v = -6 + 6 + 6v Combine like terms: -6 + 6 = 0 0 + 6v = -6 + 6 + 6v 6v = -6 + 6 + 6v Combine like terms: -6 + 6 = 0 6v = 0 + 6v 6v = 6v Add '-6v' to each side of the equation. 6v + -6v = 6v + -6v Combine like terms: 6v + -6v = 0 0 = 6v + -6v Combine like terms: 6v + -6v = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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