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Simplifying 40 = 5(4k + -3) + 5(-5 + 4k) Reorder the terms: 40 = 5(-3 + 4k) + 5(-5 + 4k) 40 = (-3 * 5 + 4k * 5) + 5(-5 + 4k) 40 = (-15 + 20k) + 5(-5 + 4k) 40 = -15 + 20k + (-5 * 5 + 4k * 5) 40 = -15 + 20k + (-25 + 20k) Reorder the terms: 40 = -15 + -25 + 20k + 20k Combine like terms: -15 + -25 = -40 40 = -40 + 20k + 20k Combine like terms: 20k + 20k = 40k 40 = -40 + 40k Solving 40 = -40 + 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. 40 + -40k = -40 + 40k + -40k Combine like terms: 40k + -40k = 0 40 + -40k = -40 + 0 40 + -40k = -40 Add '-40' to each side of the equation. 40 + -40 + -40k = -40 + -40 Combine like terms: 40 + -40 = 0 0 + -40k = -40 + -40 -40k = -40 + -40 Combine like terms: -40 + -40 = -80 -40k = -80 Divide each side by '-40'. k = 2 Simplifying k = 2
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