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Simplifying 2(4k + -5) + 9(6k + 7) = 5(5k + -8) Reorder the terms: 2(-5 + 4k) + 9(6k + 7) = 5(5k + -8) (-5 * 2 + 4k * 2) + 9(6k + 7) = 5(5k + -8) (-10 + 8k) + 9(6k + 7) = 5(5k + -8) Reorder the terms: -10 + 8k + 9(7 + 6k) = 5(5k + -8) -10 + 8k + (7 * 9 + 6k * 9) = 5(5k + -8) -10 + 8k + (63 + 54k) = 5(5k + -8) Reorder the terms: -10 + 63 + 8k + 54k = 5(5k + -8) Combine like terms: -10 + 63 = 53 53 + 8k + 54k = 5(5k + -8) Combine like terms: 8k + 54k = 62k 53 + 62k = 5(5k + -8) Reorder the terms: 53 + 62k = 5(-8 + 5k) 53 + 62k = (-8 * 5 + 5k * 5) 53 + 62k = (-40 + 25k) Solving 53 + 62k = -40 + 25k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-25k' to each side of the equation. 53 + 62k + -25k = -40 + 25k + -25k Combine like terms: 62k + -25k = 37k 53 + 37k = -40 + 25k + -25k Combine like terms: 25k + -25k = 0 53 + 37k = -40 + 0 53 + 37k = -40 Add '-53' to each side of the equation. 53 + -53 + 37k = -40 + -53 Combine like terms: 53 + -53 = 0 0 + 37k = -40 + -53 37k = -40 + -53 Combine like terms: -40 + -53 = -93 37k = -93 Divide each side by '37'. k = -2.513513514 Simplifying k = -2.513513514
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