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Simplifying -3(-7v + 3) + 8 = 5v + -4(1 + -6v) Reorder the terms: -3(3 + -7v) + 8 = 5v + -4(1 + -6v) (3 * -3 + -7v * -3) + 8 = 5v + -4(1 + -6v) (-9 + 21v) + 8 = 5v + -4(1 + -6v) Reorder the terms: -9 + 8 + 21v = 5v + -4(1 + -6v) Combine like terms: -9 + 8 = -1 -1 + 21v = 5v + -4(1 + -6v) -1 + 21v = 5v + (1 * -4 + -6v * -4) -1 + 21v = 5v + (-4 + 24v) Reorder the terms: -1 + 21v = -4 + 5v + 24v Combine like terms: 5v + 24v = 29v -1 + 21v = -4 + 29v Solving -1 + 21v = -4 + 29v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-29v' to each side of the equation. -1 + 21v + -29v = -4 + 29v + -29v Combine like terms: 21v + -29v = -8v -1 + -8v = -4 + 29v + -29v Combine like terms: 29v + -29v = 0 -1 + -8v = -4 + 0 -1 + -8v = -4 Add '1' to each side of the equation. -1 + 1 + -8v = -4 + 1 Combine like terms: -1 + 1 = 0 0 + -8v = -4 + 1 -8v = -4 + 1 Combine like terms: -4 + 1 = -3 -8v = -3 Divide each side by '-8'. v = 0.375 Simplifying v = 0.375
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