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Simplifying -2 + -7(k + 8) = 19 + 4k Reorder the terms: -2 + -7(8 + k) = 19 + 4k -2 + (8 * -7 + k * -7) = 19 + 4k -2 + (-56 + -7k) = 19 + 4k Combine like terms: -2 + -56 = -58 -58 + -7k = 19 + 4k Solving -58 + -7k = 19 + 4k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4k' to each side of the equation. -58 + -7k + -4k = 19 + 4k + -4k Combine like terms: -7k + -4k = -11k -58 + -11k = 19 + 4k + -4k Combine like terms: 4k + -4k = 0 -58 + -11k = 19 + 0 -58 + -11k = 19 Add '58' to each side of the equation. -58 + 58 + -11k = 19 + 58 Combine like terms: -58 + 58 = 0 0 + -11k = 19 + 58 -11k = 19 + 58 Combine like terms: 19 + 58 = 77 -11k = 77 Divide each side by '-11'. k = -7 Simplifying k = -7
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