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Simplifying -40 = 3(1 + -3k) + 8(7 + -3k) -40 = (1 * 3 + -3k * 3) + 8(7 + -3k) -40 = (3 + -9k) + 8(7 + -3k) -40 = 3 + -9k + (7 * 8 + -3k * 8) -40 = 3 + -9k + (56 + -24k) Reorder the terms: -40 = 3 + 56 + -9k + -24k Combine like terms: 3 + 56 = 59 -40 = 59 + -9k + -24k Combine like terms: -9k + -24k = -33k -40 = 59 + -33k Solving -40 = 59 + -33k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '33k' to each side of the equation. -40 + 33k = 59 + -33k + 33k Combine like terms: -33k + 33k = 0 -40 + 33k = 59 + 0 -40 + 33k = 59 Add '40' to each side of the equation. -40 + 40 + 33k = 59 + 40 Combine like terms: -40 + 40 = 0 0 + 33k = 59 + 40 33k = 59 + 40 Combine like terms: 59 + 40 = 99 33k = 99 Divide each side by '33'. k = 3 Simplifying k = 3
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