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Simplifying 1 + 4(2 + -3k) = 7(1 + 9k) + -8(-5k + -6) 1 + (2 * 4 + -3k * 4) = 7(1 + 9k) + -8(-5k + -6) 1 + (8 + -12k) = 7(1 + 9k) + -8(-5k + -6) Combine like terms: 1 + 8 = 9 9 + -12k = 7(1 + 9k) + -8(-5k + -6) 9 + -12k = (1 * 7 + 9k * 7) + -8(-5k + -6) 9 + -12k = (7 + 63k) + -8(-5k + -6) Reorder the terms: 9 + -12k = 7 + 63k + -8(-6 + -5k) 9 + -12k = 7 + 63k + (-6 * -8 + -5k * -8) 9 + -12k = 7 + 63k + (48 + 40k) Reorder the terms: 9 + -12k = 7 + 48 + 63k + 40k Combine like terms: 7 + 48 = 55 9 + -12k = 55 + 63k + 40k Combine like terms: 63k + 40k = 103k 9 + -12k = 55 + 103k Solving 9 + -12k = 55 + 103k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-103k' to each side of the equation. 9 + -12k + -103k = 55 + 103k + -103k Combine like terms: -12k + -103k = -115k 9 + -115k = 55 + 103k + -103k Combine like terms: 103k + -103k = 0 9 + -115k = 55 + 0 9 + -115k = 55 Add '-9' to each side of the equation. 9 + -9 + -115k = 55 + -9 Combine like terms: 9 + -9 = 0 0 + -115k = 55 + -9 -115k = 55 + -9 Combine like terms: 55 + -9 = 46 -115k = 46 Divide each side by '-115'. k = -0.4 Simplifying k = -0.4
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