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Simplifying 5(1 + -7k) = 7 + -8(2k + 5) (1 * 5 + -7k * 5) = 7 + -8(2k + 5) (5 + -35k) = 7 + -8(2k + 5) Reorder the terms: 5 + -35k = 7 + -8(5 + 2k) 5 + -35k = 7 + (5 * -8 + 2k * -8) 5 + -35k = 7 + (-40 + -16k) Combine like terms: 7 + -40 = -33 5 + -35k = -33 + -16k Solving 5 + -35k = -33 + -16k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '16k' to each side of the equation. 5 + -35k + 16k = -33 + -16k + 16k Combine like terms: -35k + 16k = -19k 5 + -19k = -33 + -16k + 16k Combine like terms: -16k + 16k = 0 5 + -19k = -33 + 0 5 + -19k = -33 Add '-5' to each side of the equation. 5 + -5 + -19k = -33 + -5 Combine like terms: 5 + -5 = 0 0 + -19k = -33 + -5 -19k = -33 + -5 Combine like terms: -33 + -5 = -38 -19k = -38 Divide each side by '-19'. k = 2 Simplifying k = 2
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