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Simplifying 2(4v + -3) + -8(v + -4) = -1v + 5(v + -2) Reorder the terms: 2(-3 + 4v) + -8(v + -4) = -1v + 5(v + -2) (-3 * 2 + 4v * 2) + -8(v + -4) = -1v + 5(v + -2) (-6 + 8v) + -8(v + -4) = -1v + 5(v + -2) Reorder the terms: -6 + 8v + -8(-4 + v) = -1v + 5(v + -2) -6 + 8v + (-4 * -8 + v * -8) = -1v + 5(v + -2) -6 + 8v + (32 + -8v) = -1v + 5(v + -2) Reorder the terms: -6 + 32 + 8v + -8v = -1v + 5(v + -2) Combine like terms: -6 + 32 = 26 26 + 8v + -8v = -1v + 5(v + -2) Combine like terms: 8v + -8v = 0 26 + 0 = -1v + 5(v + -2) 26 = -1v + 5(v + -2) Reorder the terms: 26 = -1v + 5(-2 + v) 26 = -1v + (-2 * 5 + v * 5) 26 = -1v + (-10 + 5v) Reorder the terms: 26 = -10 + -1v + 5v Combine like terms: -1v + 5v = 4v 26 = -10 + 4v Solving 26 = -10 + 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. 26 + -4v = -10 + 4v + -4v Combine like terms: 4v + -4v = 0 26 + -4v = -10 + 0 26 + -4v = -10 Add '-26' to each side of the equation. 26 + -26 + -4v = -10 + -26 Combine like terms: 26 + -26 = 0 0 + -4v = -10 + -26 -4v = -10 + -26 Combine like terms: -10 + -26 = -36 -4v = -36 Divide each side by '-4'. v = 9 Simplifying v = 9
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