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Simplifying 5(k + -8) = 7(3k + 1) + 17 Reorder the terms: 5(-8 + k) = 7(3k + 1) + 17 (-8 * 5 + k * 5) = 7(3k + 1) + 17 (-40 + 5k) = 7(3k + 1) + 17 Reorder the terms: -40 + 5k = 7(1 + 3k) + 17 -40 + 5k = (1 * 7 + 3k * 7) + 17 -40 + 5k = (7 + 21k) + 17 Reorder the terms: -40 + 5k = 7 + 17 + 21k Combine like terms: 7 + 17 = 24 -40 + 5k = 24 + 21k Solving -40 + 5k = 24 + 21k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-21k' to each side of the equation. -40 + 5k + -21k = 24 + 21k + -21k Combine like terms: 5k + -21k = -16k -40 + -16k = 24 + 21k + -21k Combine like terms: 21k + -21k = 0 -40 + -16k = 24 + 0 -40 + -16k = 24 Add '40' to each side of the equation. -40 + 40 + -16k = 24 + 40 Combine like terms: -40 + 40 = 0 0 + -16k = 24 + 40 -16k = 24 + 40 Combine like terms: 24 + 40 = 64 -16k = 64 Divide each side by '-16'. k = -4 Simplifying k = -4
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