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Simplifying 4(k + -4) + -5k = 9 + -8(k + 9) Reorder the terms: 4(-4 + k) + -5k = 9 + -8(k + 9) (-4 * 4 + k * 4) + -5k = 9 + -8(k + 9) (-16 + 4k) + -5k = 9 + -8(k + 9) Combine like terms: 4k + -5k = -1k -16 + -1k = 9 + -8(k + 9) Reorder the terms: -16 + -1k = 9 + -8(9 + k) -16 + -1k = 9 + (9 * -8 + k * -8) -16 + -1k = 9 + (-72 + -8k) Combine like terms: 9 + -72 = -63 -16 + -1k = -63 + -8k Solving -16 + -1k = -63 + -8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '8k' to each side of the equation. -16 + -1k + 8k = -63 + -8k + 8k Combine like terms: -1k + 8k = 7k -16 + 7k = -63 + -8k + 8k Combine like terms: -8k + 8k = 0 -16 + 7k = -63 + 0 -16 + 7k = -63 Add '16' to each side of the equation. -16 + 16 + 7k = -63 + 16 Combine like terms: -16 + 16 = 0 0 + 7k = -63 + 16 7k = -63 + 16 Combine like terms: -63 + 16 = -47 7k = -47 Divide each side by '7'. k = -6.714285714 Simplifying k = -6.714285714
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