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Simplifying 15(v + 3) + -3v = (4v + 1) + -7 Reorder the terms: 15(3 + v) + -3v = (4v + 1) + -7 (3 * 15 + v * 15) + -3v = (4v + 1) + -7 (45 + 15v) + -3v = (4v + 1) + -7 Combine like terms: 15v + -3v = 12v 45 + 12v = (4v + 1) + -7 Reorder the terms: 45 + 12v = (1 + 4v) + -7 Remove parenthesis around (1 + 4v) 45 + 12v = 1 + 4v + -7 Reorder the terms: 45 + 12v = 1 + -7 + 4v Combine like terms: 1 + -7 = -6 45 + 12v = -6 + 4v Solving 45 + 12v = -6 + 4v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4v' to each side of the equation. 45 + 12v + -4v = -6 + 4v + -4v Combine like terms: 12v + -4v = 8v 45 + 8v = -6 + 4v + -4v Combine like terms: 4v + -4v = 0 45 + 8v = -6 + 0 45 + 8v = -6 Add '-45' to each side of the equation. 45 + -45 + 8v = -6 + -45 Combine like terms: 45 + -45 = 0 0 + 8v = -6 + -45 8v = -6 + -45 Combine like terms: -6 + -45 = -51 8v = -51 Divide each side by '8'. v = -6.375 Simplifying v = -6.375
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