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Simplifying 5(k + -4) + -4(k + 1) + -14 = -31 Reorder the terms: 5(-4 + k) + -4(k + 1) + -14 = -31 (-4 * 5 + k * 5) + -4(k + 1) + -14 = -31 (-20 + 5k) + -4(k + 1) + -14 = -31 Reorder the terms: -20 + 5k + -4(1 + k) + -14 = -31 -20 + 5k + (1 * -4 + k * -4) + -14 = -31 -20 + 5k + (-4 + -4k) + -14 = -31 Reorder the terms: -20 + -4 + -14 + 5k + -4k = -31 Combine like terms: -20 + -4 = -24 -24 + -14 + 5k + -4k = -31 Combine like terms: -24 + -14 = -38 -38 + 5k + -4k = -31 Combine like terms: 5k + -4k = 1k -38 + 1k = -31 Solving -38 + 1k = -31 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '38' to each side of the equation. -38 + 38 + 1k = -31 + 38 Combine like terms: -38 + 38 = 0 0 + 1k = -31 + 38 1k = -31 + 38 Combine like terms: -31 + 38 = 7 1k = 7 Divide each side by '1'. k = 7 Simplifying k = 7
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