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Simplifying 5v + 7 = 6(v + -2) + -4(2v + -3) Reorder the terms: 7 + 5v = 6(v + -2) + -4(2v + -3) Reorder the terms: 7 + 5v = 6(-2 + v) + -4(2v + -3) 7 + 5v = (-2 * 6 + v * 6) + -4(2v + -3) 7 + 5v = (-12 + 6v) + -4(2v + -3) Reorder the terms: 7 + 5v = -12 + 6v + -4(-3 + 2v) 7 + 5v = -12 + 6v + (-3 * -4 + 2v * -4) 7 + 5v = -12 + 6v + (12 + -8v) Reorder the terms: 7 + 5v = -12 + 12 + 6v + -8v Combine like terms: -12 + 12 = 0 7 + 5v = 0 + 6v + -8v 7 + 5v = 6v + -8v Combine like terms: 6v + -8v = -2v 7 + 5v = -2v Solving 7 + 5v = -2v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2v' to each side of the equation. 7 + 5v + 2v = -2v + 2v Combine like terms: 5v + 2v = 7v 7 + 7v = -2v + 2v Combine like terms: -2v + 2v = 0 7 + 7v = 0 Add '-7' to each side of the equation. 7 + -7 + 7v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 7v = 0 + -7 7v = 0 + -7 Combine like terms: 0 + -7 = -7 7v = -7 Divide each side by '7'. v = -1 Simplifying v = -1
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