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Simplifying 7(7k + -7) + -1 = 38 + 5k Reorder the terms: 7(-7 + 7k) + -1 = 38 + 5k (-7 * 7 + 7k * 7) + -1 = 38 + 5k (-49 + 49k) + -1 = 38 + 5k Reorder the terms: -49 + -1 + 49k = 38 + 5k Combine like terms: -49 + -1 = -50 -50 + 49k = 38 + 5k Solving -50 + 49k = 38 + 5k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-5k' to each side of the equation. -50 + 49k + -5k = 38 + 5k + -5k Combine like terms: 49k + -5k = 44k -50 + 44k = 38 + 5k + -5k Combine like terms: 5k + -5k = 0 -50 + 44k = 38 + 0 -50 + 44k = 38 Add '50' to each side of the equation. -50 + 50 + 44k = 38 + 50 Combine like terms: -50 + 50 = 0 0 + 44k = 38 + 50 44k = 38 + 50 Combine like terms: 38 + 50 = 88 44k = 88 Divide each side by '44'. k = 2 Simplifying k = 2
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