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Simplifying -5(1 + -1k) + -2 = 5 + -1(2k + 1)(-2) (1 * -5 + -1k * -5) + -2 = 5 + -1(2k + 1)(-2) (-5 + 5k) + -2 = 5 + -1(2k + 1)(-2) Reorder the terms: -5 + -2 + 5k = 5 + -1(2k + 1)(-2) Combine like terms: -5 + -2 = -7 -7 + 5k = 5 + -1(2k + 1)(-2) Reorder the terms: -7 + 5k = 5 + -1(1 + 2k)(-2) Reorder the terms for easier multiplication: -7 + 5k = 5 + -1 * -2(1 + 2k) Multiply -1 * -2 -7 + 5k = 5 + 2(1 + 2k) -7 + 5k = 5 + (1 * 2 + 2k * 2) -7 + 5k = 5 + (2 + 4k) Combine like terms: 5 + 2 = 7 -7 + 5k = 7 + 4k Solving -7 + 5k = 7 + 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. -7 + 5k + -4k = 7 + 4k + -4k Combine like terms: 5k + -4k = 1k -7 + 1k = 7 + 4k + -4k Combine like terms: 4k + -4k = 0 -7 + 1k = 7 + 0 -7 + 1k = 7 Add '7' to each side of the equation. -7 + 7 + 1k = 7 + 7 Combine like terms: -7 + 7 = 0 0 + 1k = 7 + 7 1k = 7 + 7 Combine like terms: 7 + 7 = 14 1k = 14 Divide each side by '1'. k = 14 Simplifying k = 14
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