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Simplifying -31 + 8k = 5(8 + 8k) + -7 -31 + 8k = (8 * 5 + 8k * 5) + -7 -31 + 8k = (40 + 40k) + -7 Reorder the terms: -31 + 8k = 40 + -7 + 40k Combine like terms: 40 + -7 = 33 -31 + 8k = 33 + 40k Solving -31 + 8k = 33 + 40k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-40k' to each side of the equation. -31 + 8k + -40k = 33 + 40k + -40k Combine like terms: 8k + -40k = -32k -31 + -32k = 33 + 40k + -40k Combine like terms: 40k + -40k = 0 -31 + -32k = 33 + 0 -31 + -32k = 33 Add '31' to each side of the equation. -31 + 31 + -32k = 33 + 31 Combine like terms: -31 + 31 = 0 0 + -32k = 33 + 31 -32k = 33 + 31 Combine like terms: 33 + 31 = 64 -32k = 64 Divide each side by '-32'. k = -2 Simplifying k = -2
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