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Simplifying 1 + -8(5k + 9) = 7k + 1 Reorder the terms: 1 + -8(9 + 5k) = 7k + 1 1 + (9 * -8 + 5k * -8) = 7k + 1 1 + (-72 + -40k) = 7k + 1 Combine like terms: 1 + -72 = -71 -71 + -40k = 7k + 1 Reorder the terms: -71 + -40k = 1 + 7k Solving -71 + -40k = 1 + 7k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7k' to each side of the equation. -71 + -40k + -7k = 1 + 7k + -7k Combine like terms: -40k + -7k = -47k -71 + -47k = 1 + 7k + -7k Combine like terms: 7k + -7k = 0 -71 + -47k = 1 + 0 -71 + -47k = 1 Add '71' to each side of the equation. -71 + 71 + -47k = 1 + 71 Combine like terms: -71 + 71 = 0 0 + -47k = 1 + 71 -47k = 1 + 71 Combine like terms: 1 + 71 = 72 -47k = 72 Divide each side by '-47'. k = -1.531914894 Simplifying k = -1.531914894
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