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Simplifying 0.75k + -1(k + 0.25) = 0.625(k + 1) Reorder the terms: 0.75k + -1(0.25 + k) = 0.625(k + 1) 0.75k + (0.25 * -1 + k * -1) = 0.625(k + 1) 0.75k + (-0.25 + -1k) = 0.625(k + 1) Reorder the terms: -0.25 + 0.75k + -1k = 0.625(k + 1) Combine like terms: 0.75k + -1k = -0.25k -0.25 + -0.25k = 0.625(k + 1) Reorder the terms: -0.25 + -0.25k = 0.625(1 + k) -0.25 + -0.25k = (1 * 0.625 + k * 0.625) -0.25 + -0.25k = (0.625 + 0.625k) Solving -0.25 + -0.25k = 0.625 + 0.625k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.625k' to each side of the equation. -0.25 + -0.25k + -0.625k = 0.625 + 0.625k + -0.625k Combine like terms: -0.25k + -0.625k = -0.875k -0.25 + -0.875k = 0.625 + 0.625k + -0.625k Combine like terms: 0.625k + -0.625k = 0.000 -0.25 + -0.875k = 0.625 + 0.000 -0.25 + -0.875k = 0.625 Add '0.25' to each side of the equation. -0.25 + 0.25 + -0.875k = 0.625 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.875k = 0.625 + 0.25 -0.875k = 0.625 + 0.25 Combine like terms: 0.625 + 0.25 = 0.875 -0.875k = 0.875 Divide each side by '-0.875'. k = -1 Simplifying k = -1
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