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Simplifying (3x + 2) + -1(v + 1) = x + (2x + 3) Reorder the terms: (2 + 3x) + -1(v + 1) = x + (2x + 3) Remove parenthesis around (2 + 3x) 2 + 3x + -1(v + 1) = x + (2x + 3) Reorder the terms: 2 + 3x + -1(1 + v) = x + (2x + 3) 2 + 3x + (1 * -1 + v * -1) = x + (2x + 3) 2 + 3x + (-1 + -1v) = x + (2x + 3) Reorder the terms: 2 + -1 + -1v + 3x = x + (2x + 3) Combine like terms: 2 + -1 = 1 1 + -1v + 3x = x + (2x + 3) Reorder the terms: 1 + -1v + 3x = x + (3 + 2x) Remove parenthesis around (3 + 2x) 1 + -1v + 3x = x + 3 + 2x Reorder the terms: 1 + -1v + 3x = 3 + x + 2x Combine like terms: x + 2x = 3x 1 + -1v + 3x = 3 + 3x Add '-3x' to each side of the equation. 1 + -1v + 3x + -3x = 3 + 3x + -3x Combine like terms: 3x + -3x = 0 1 + -1v + 0 = 3 + 3x + -3x 1 + -1v = 3 + 3x + -3x Combine like terms: 3x + -3x = 0 1 + -1v = 3 + 0 1 + -1v = 3 Solving 1 + -1v = 3 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1v = 3 + -1 Combine like terms: 1 + -1 = 0 0 + -1v = 3 + -1 -1v = 3 + -1 Combine like terms: 3 + -1 = 2 -1v = 2 Divide each side by '-1'. v = -2 Simplifying v = -2
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