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Simplifying 4(k + -4) + -8(k + 4) = 5(3k + -4) + -9(3k + 4) Reorder the terms: 4(-4 + k) + -8(k + 4) = 5(3k + -4) + -9(3k + 4) (-4 * 4 + k * 4) + -8(k + 4) = 5(3k + -4) + -9(3k + 4) (-16 + 4k) + -8(k + 4) = 5(3k + -4) + -9(3k + 4) Reorder the terms: -16 + 4k + -8(4 + k) = 5(3k + -4) + -9(3k + 4) -16 + 4k + (4 * -8 + k * -8) = 5(3k + -4) + -9(3k + 4) -16 + 4k + (-32 + -8k) = 5(3k + -4) + -9(3k + 4) Reorder the terms: -16 + -32 + 4k + -8k = 5(3k + -4) + -9(3k + 4) Combine like terms: -16 + -32 = -48 -48 + 4k + -8k = 5(3k + -4) + -9(3k + 4) Combine like terms: 4k + -8k = -4k -48 + -4k = 5(3k + -4) + -9(3k + 4) Reorder the terms: -48 + -4k = 5(-4 + 3k) + -9(3k + 4) -48 + -4k = (-4 * 5 + 3k * 5) + -9(3k + 4) -48 + -4k = (-20 + 15k) + -9(3k + 4) Reorder the terms: -48 + -4k = -20 + 15k + -9(4 + 3k) -48 + -4k = -20 + 15k + (4 * -9 + 3k * -9) -48 + -4k = -20 + 15k + (-36 + -27k) Reorder the terms: -48 + -4k = -20 + -36 + 15k + -27k Combine like terms: -20 + -36 = -56 -48 + -4k = -56 + 15k + -27k Combine like terms: 15k + -27k = -12k -48 + -4k = -56 + -12k Solving -48 + -4k = -56 + -12k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '12k' to each side of the equation. -48 + -4k + 12k = -56 + -12k + 12k Combine like terms: -4k + 12k = 8k -48 + 8k = -56 + -12k + 12k Combine like terms: -12k + 12k = 0 -48 + 8k = -56 + 0 -48 + 8k = -56 Add '48' to each side of the equation. -48 + 48 + 8k = -56 + 48 Combine like terms: -48 + 48 = 0 0 + 8k = -56 + 48 8k = -56 + 48 Combine like terms: -56 + 48 = -8 8k = -8 Divide each side by '8'. k = -1 Simplifying k = -1
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