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Simplifying 40 = -8(1 + 5k) + -2(k + -3) 40 = (1 * -8 + 5k * -8) + -2(k + -3) 40 = (-8 + -40k) + -2(k + -3) Reorder the terms: 40 = -8 + -40k + -2(-3 + k) 40 = -8 + -40k + (-3 * -2 + k * -2) 40 = -8 + -40k + (6 + -2k) Reorder the terms: 40 = -8 + 6 + -40k + -2k Combine like terms: -8 + 6 = -2 40 = -2 + -40k + -2k Combine like terms: -40k + -2k = -42k 40 = -2 + -42k Solving 40 = -2 + -42k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '42k' to each side of the equation. 40 + 42k = -2 + -42k + 42k Combine like terms: -42k + 42k = 0 40 + 42k = -2 + 0 40 + 42k = -2 Add '-40' to each side of the equation. 40 + -40 + 42k = -2 + -40 Combine like terms: 40 + -40 = 0 0 + 42k = -2 + -40 42k = -2 + -40 Combine like terms: -2 + -40 = -42 42k = -42 Divide each side by '42'. k = -1 Simplifying k = -1
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