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Simplifying 8(2 + -5k) + -4k = 1 + 5(-6 + -7k) (2 * 8 + -5k * 8) + -4k = 1 + 5(-6 + -7k) (16 + -40k) + -4k = 1 + 5(-6 + -7k) Combine like terms: -40k + -4k = -44k 16 + -44k = 1 + 5(-6 + -7k) 16 + -44k = 1 + (-6 * 5 + -7k * 5) 16 + -44k = 1 + (-30 + -35k) Combine like terms: 1 + -30 = -29 16 + -44k = -29 + -35k Solving 16 + -44k = -29 + -35k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '35k' to each side of the equation. 16 + -44k + 35k = -29 + -35k + 35k Combine like terms: -44k + 35k = -9k 16 + -9k = -29 + -35k + 35k Combine like terms: -35k + 35k = 0 16 + -9k = -29 + 0 16 + -9k = -29 Add '-16' to each side of the equation. 16 + -16 + -9k = -29 + -16 Combine like terms: 16 + -16 = 0 0 + -9k = -29 + -16 -9k = -29 + -16 Combine like terms: -29 + -16 = -45 -9k = -45 Divide each side by '-9'. k = 5 Simplifying k = 5
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