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Simplifying -6(-9 + -7r) + -8(8 + 2k) = 0 (-9 * -6 + -7r * -6) + -8(8 + 2k) = 0 (54 + 42r) + -8(8 + 2k) = 0 54 + 42r + (8 * -8 + 2k * -8) = 0 54 + 42r + (-64 + -16k) = 0 Reorder the terms: 54 + -64 + -16k + 42r = 0 Combine like terms: 54 + -64 = -10 -10 + -16k + 42r = 0 Solving -10 + -16k + 42r = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '10' to each side of the equation. -10 + -16k + 10 + 42r = 0 + 10 Reorder the terms: -10 + 10 + -16k + 42r = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -16k + 42r = 0 + 10 -16k + 42r = 0 + 10 Combine like terms: 0 + 10 = 10 -16k + 42r = 10 Add '-42r' to each side of the equation. -16k + 42r + -42r = 10 + -42r Combine like terms: 42r + -42r = 0 -16k + 0 = 10 + -42r -16k = 10 + -42r Divide each side by '-16'. k = -0.625 + 2.625r Simplifying k = -0.625 + 2.625r
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