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Simplifying 7(4k + -6) + 5(1 + -4k) = 19 Reorder the terms: 7(-6 + 4k) + 5(1 + -4k) = 19 (-6 * 7 + 4k * 7) + 5(1 + -4k) = 19 (-42 + 28k) + 5(1 + -4k) = 19 -42 + 28k + (1 * 5 + -4k * 5) = 19 -42 + 28k + (5 + -20k) = 19 Reorder the terms: -42 + 5 + 28k + -20k = 19 Combine like terms: -42 + 5 = -37 -37 + 28k + -20k = 19 Combine like terms: 28k + -20k = 8k -37 + 8k = 19 Solving -37 + 8k = 19 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '37' to each side of the equation. -37 + 37 + 8k = 19 + 37 Combine like terms: -37 + 37 = 0 0 + 8k = 19 + 37 8k = 19 + 37 Combine like terms: 19 + 37 = 56 8k = 56 Divide each side by '8'. k = 7 Simplifying k = 7
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