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Simplifying -41 = -8(8 + 5k) + -7(-5 + -3k) -41 = (8 * -8 + 5k * -8) + -7(-5 + -3k) -41 = (-64 + -40k) + -7(-5 + -3k) -41 = -64 + -40k + (-5 * -7 + -3k * -7) -41 = -64 + -40k + (35 + 21k) Reorder the terms: -41 = -64 + 35 + -40k + 21k Combine like terms: -64 + 35 = -29 -41 = -29 + -40k + 21k Combine like terms: -40k + 21k = -19k -41 = -29 + -19k Solving -41 = -29 + -19k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '19k' to each side of the equation. -41 + 19k = -29 + -19k + 19k Combine like terms: -19k + 19k = 0 -41 + 19k = -29 + 0 -41 + 19k = -29 Add '41' to each side of the equation. -41 + 41 + 19k = -29 + 41 Combine like terms: -41 + 41 = 0 0 + 19k = -29 + 41 19k = -29 + 41 Combine like terms: -29 + 41 = 12 19k = 12 Divide each side by '19'. k = 0.6315789474 Simplifying k = 0.6315789474
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