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Simplifying 4(4k + -0.2) = 4(k + 1.1) + -2(4k + -3.1) Reorder the terms: 4(-0.2 + 4k) = 4(k + 1.1) + -2(4k + -3.1) (-0.2 * 4 + 4k * 4) = 4(k + 1.1) + -2(4k + -3.1) (-0.8 + 16k) = 4(k + 1.1) + -2(4k + -3.1) Reorder the terms: -0.8 + 16k = 4(1.1 + k) + -2(4k + -3.1) -0.8 + 16k = (1.1 * 4 + k * 4) + -2(4k + -3.1) -0.8 + 16k = (4.4 + 4k) + -2(4k + -3.1) Reorder the terms: -0.8 + 16k = 4.4 + 4k + -2(-3.1 + 4k) -0.8 + 16k = 4.4 + 4k + (-3.1 * -2 + 4k * -2) -0.8 + 16k = 4.4 + 4k + (6.2 + -8k) Reorder the terms: -0.8 + 16k = 4.4 + 6.2 + 4k + -8k Combine like terms: 4.4 + 6.2 = 10.6 -0.8 + 16k = 10.6 + 4k + -8k Combine like terms: 4k + -8k = -4k -0.8 + 16k = 10.6 + -4k Solving -0.8 + 16k = 10.6 + -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. -0.8 + 16k + 4k = 10.6 + -4k + 4k Combine like terms: 16k + 4k = 20k -0.8 + 20k = 10.6 + -4k + 4k Combine like terms: -4k + 4k = 0 -0.8 + 20k = 10.6 + 0 -0.8 + 20k = 10.6 Add '0.8' to each side of the equation. -0.8 + 0.8 + 20k = 10.6 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 20k = 10.6 + 0.8 20k = 10.6 + 0.8 Combine like terms: 10.6 + 0.8 = 11.4 20k = 11.4 Divide each side by '20'. k = 0.57 Simplifying k = 0.57
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