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Simplifying -9 = -5(8 + -2k) + 3(k + -7) -9 = (8 * -5 + -2k * -5) + 3(k + -7) -9 = (-40 + 10k) + 3(k + -7) Reorder the terms: -9 = -40 + 10k + 3(-7 + k) -9 = -40 + 10k + (-7 * 3 + k * 3) -9 = -40 + 10k + (-21 + 3k) Reorder the terms: -9 = -40 + -21 + 10k + 3k Combine like terms: -40 + -21 = -61 -9 = -61 + 10k + 3k Combine like terms: 10k + 3k = 13k -9 = -61 + 13k Solving -9 = -61 + 13k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-13k' to each side of the equation. -9 + -13k = -61 + 13k + -13k Combine like terms: 13k + -13k = 0 -9 + -13k = -61 + 0 -9 + -13k = -61 Add '9' to each side of the equation. -9 + 9 + -13k = -61 + 9 Combine like terms: -9 + 9 = 0 0 + -13k = -61 + 9 -13k = -61 + 9 Combine like terms: -61 + 9 = -52 -13k = -52 Divide each side by '-13'. k = 4 Simplifying k = 4
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