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Simplifying 34.8k + 0.2(1k + -4) = 1.2 + -9(2 + -3k) Reorder the terms: 34.8k + 0.2(-4 + 1k) = 1.2 + -9(2 + -3k) 34.8k + (-4 * 0.2 + 1k * 0.2) = 1.2 + -9(2 + -3k) 34.8k + (-0.8 + 0.2k) = 1.2 + -9(2 + -3k) Reorder the terms: -0.8 + 34.8k + 0.2k = 1.2 + -9(2 + -3k) Combine like terms: 34.8k + 0.2k = 35k -0.8 + 35k = 1.2 + -9(2 + -3k) -0.8 + 35k = 1.2 + (2 * -9 + -3k * -9) -0.8 + 35k = 1.2 + (-18 + 27k) Combine like terms: 1.2 + -18 = -16.8 -0.8 + 35k = -16.8 + 27k Solving -0.8 + 35k = -16.8 + 27k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-27k' to each side of the equation. -0.8 + 35k + -27k = -16.8 + 27k + -27k Combine like terms: 35k + -27k = 8k -0.8 + 8k = -16.8 + 27k + -27k Combine like terms: 27k + -27k = 0 -0.8 + 8k = -16.8 + 0 -0.8 + 8k = -16.8 Add '0.8' to each side of the equation. -0.8 + 0.8 + 8k = -16.8 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 8k = -16.8 + 0.8 8k = -16.8 + 0.8 Combine like terms: -16.8 + 0.8 = -16 8k = -16 Divide each side by '8'. k = -2 Simplifying k = -2
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