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Simplifying 46 + 3k + -1 = 4(5k + -6) + -3(k + -9) Reorder the terms: 46 + -1 + 3k = 4(5k + -6) + -3(k + -9) Combine like terms: 46 + -1 = 45 45 + 3k = 4(5k + -6) + -3(k + -9) Reorder the terms: 45 + 3k = 4(-6 + 5k) + -3(k + -9) 45 + 3k = (-6 * 4 + 5k * 4) + -3(k + -9) 45 + 3k = (-24 + 20k) + -3(k + -9) Reorder the terms: 45 + 3k = -24 + 20k + -3(-9 + k) 45 + 3k = -24 + 20k + (-9 * -3 + k * -3) 45 + 3k = -24 + 20k + (27 + -3k) Reorder the terms: 45 + 3k = -24 + 27 + 20k + -3k Combine like terms: -24 + 27 = 3 45 + 3k = 3 + 20k + -3k Combine like terms: 20k + -3k = 17k 45 + 3k = 3 + 17k Solving 45 + 3k = 3 + 17k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-17k' to each side of the equation. 45 + 3k + -17k = 3 + 17k + -17k Combine like terms: 3k + -17k = -14k 45 + -14k = 3 + 17k + -17k Combine like terms: 17k + -17k = 0 45 + -14k = 3 + 0 45 + -14k = 3 Add '-45' to each side of the equation. 45 + -45 + -14k = 3 + -45 Combine like terms: 45 + -45 = 0 0 + -14k = 3 + -45 -14k = 3 + -45 Combine like terms: 3 + -45 = -42 -14k = -42 Divide each side by '-14'. k = 3 Simplifying k = 3
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