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Simplifying 4(k + -4) + -8(k + 4) = (3k + -4) + -9(3k + 4) Reorder the terms: 4(-4 + k) + -8(k + 4) = (3k + -4) + -9(3k + 4) (-4 * 4 + k * 4) + -8(k + 4) = (3k + -4) + -9(3k + 4) (-16 + 4k) + -8(k + 4) = (3k + -4) + -9(3k + 4) Reorder the terms: -16 + 4k + -8(4 + k) = (3k + -4) + -9(3k + 4) -16 + 4k + (4 * -8 + k * -8) = (3k + -4) + -9(3k + 4) -16 + 4k + (-32 + -8k) = (3k + -4) + -9(3k + 4) Reorder the terms: -16 + -32 + 4k + -8k = (3k + -4) + -9(3k + 4) Combine like terms: -16 + -32 = -48 -48 + 4k + -8k = (3k + -4) + -9(3k + 4) Combine like terms: 4k + -8k = -4k -48 + -4k = (3k + -4) + -9(3k + 4) Reorder the terms: -48 + -4k = (-4 + 3k) + -9(3k + 4) Remove parenthesis around (-4 + 3k) -48 + -4k = -4 + 3k + -9(3k + 4) Reorder the terms: -48 + -4k = -4 + 3k + -9(4 + 3k) -48 + -4k = -4 + 3k + (4 * -9 + 3k * -9) -48 + -4k = -4 + 3k + (-36 + -27k) Reorder the terms: -48 + -4k = -4 + -36 + 3k + -27k Combine like terms: -4 + -36 = -40 -48 + -4k = -40 + 3k + -27k Combine like terms: 3k + -27k = -24k -48 + -4k = -40 + -24k Solving -48 + -4k = -40 + -24k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '24k' to each side of the equation. -48 + -4k + 24k = -40 + -24k + 24k Combine like terms: -4k + 24k = 20k -48 + 20k = -40 + -24k + 24k Combine like terms: -24k + 24k = 0 -48 + 20k = -40 + 0 -48 + 20k = -40 Add '48' to each side of the equation. -48 + 48 + 20k = -40 + 48 Combine like terms: -48 + 48 = 0 0 + 20k = -40 + 48 20k = -40 + 48 Combine like terms: -40 + 48 = 8 20k = 8 Divide each side by '20'. k = 0.4 Simplifying k = 0.4
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