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Simplifying -8(1 + 2k) + 3(k + -8) = -19 (1 * -8 + 2k * -8) + 3(k + -8) = -19 (-8 + -16k) + 3(k + -8) = -19 Reorder the terms: -8 + -16k + 3(-8 + k) = -19 -8 + -16k + (-8 * 3 + k * 3) = -19 -8 + -16k + (-24 + 3k) = -19 Reorder the terms: -8 + -24 + -16k + 3k = -19 Combine like terms: -8 + -24 = -32 -32 + -16k + 3k = -19 Combine like terms: -16k + 3k = -13k -32 + -13k = -19 Solving -32 + -13k = -19 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + -13k = -19 + 32 Combine like terms: -32 + 32 = 0 0 + -13k = -19 + 32 -13k = -19 + 32 Combine like terms: -19 + 32 = 13 -13k = 13 Divide each side by '-13'. k = -1 Simplifying k = -1
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