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Simplifying (2k + -8) * 5 + 2k = 20k + -100 Reorder the terms: (-8 + 2k) * 5 + 2k = 20k + -100 Reorder the terms for easier multiplication: 5(-8 + 2k) + 2k = 20k + -100 (-8 * 5 + 2k * 5) + 2k = 20k + -100 (-40 + 10k) + 2k = 20k + -100 Combine like terms: 10k + 2k = 12k -40 + 12k = 20k + -100 Reorder the terms: -40 + 12k = -100 + 20k Solving -40 + 12k = -100 + 20k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-20k' to each side of the equation. -40 + 12k + -20k = -100 + 20k + -20k Combine like terms: 12k + -20k = -8k -40 + -8k = -100 + 20k + -20k Combine like terms: 20k + -20k = 0 -40 + -8k = -100 + 0 -40 + -8k = -100 Add '40' to each side of the equation. -40 + 40 + -8k = -100 + 40 Combine like terms: -40 + 40 = 0 0 + -8k = -100 + 40 -8k = -100 + 40 Combine like terms: -100 + 40 = -60 -8k = -60 Divide each side by '-8'. k = 7.5 Simplifying k = 7.5
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