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Simplifying (K + 1) * x + -1(2k + 8) = 0 Reorder the terms: (1 + K) * x + -1(2k + 8) = 0 Reorder the terms for easier multiplication: x(1 + K) + -1(2k + 8) = 0 (1 * x + K * x) + -1(2k + 8) = 0 (1x + xK) + -1(2k + 8) = 0 Reorder the terms: 1x + xK + -1(8 + 2k) = 0 1x + xK + (8 * -1 + 2k * -1) = 0 1x + xK + (-8 + -2k) = 0 Reorder the terms: -8 + -2k + 1x + xK = 0 Solving -8 + -2k + 1x + xK = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '8' to each side of the equation. -8 + -2k + 1x + 8 + xK = 0 + 8 Reorder the terms: -8 + 8 + -2k + 1x + xK = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -2k + 1x + xK = 0 + 8 -2k + 1x + xK = 0 + 8 Combine like terms: 0 + 8 = 8 -2k + 1x + xK = 8 Add '-1x' to each side of the equation. -2k + 1x + -1x + xK = 8 + -1x Combine like terms: 1x + -1x = 0 -2k + 0 + xK = 8 + -1x -2k + xK = 8 + -1x Add '-1xK' to each side of the equation. -2k + xK + -1xK = 8 + -1x + -1xK Combine like terms: xK + -1xK = 0 -2k + 0 = 8 + -1x + -1xK -2k = 8 + -1x + -1xK Divide each side by '-2'. k = -4 + 0.5x + 0.5xK Simplifying k = -4 + 0.5x + 0.5xK
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