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Simplifying 2(4k + -2) + -5(5k + 1) = 2 + -3(k + 3) Reorder the terms: 2(-2 + 4k) + -5(5k + 1) = 2 + -3(k + 3) (-2 * 2 + 4k * 2) + -5(5k + 1) = 2 + -3(k + 3) (-4 + 8k) + -5(5k + 1) = 2 + -3(k + 3) Reorder the terms: -4 + 8k + -5(1 + 5k) = 2 + -3(k + 3) -4 + 8k + (1 * -5 + 5k * -5) = 2 + -3(k + 3) -4 + 8k + (-5 + -25k) = 2 + -3(k + 3) Reorder the terms: -4 + -5 + 8k + -25k = 2 + -3(k + 3) Combine like terms: -4 + -5 = -9 -9 + 8k + -25k = 2 + -3(k + 3) Combine like terms: 8k + -25k = -17k -9 + -17k = 2 + -3(k + 3) Reorder the terms: -9 + -17k = 2 + -3(3 + k) -9 + -17k = 2 + (3 * -3 + k * -3) -9 + -17k = 2 + (-9 + -3k) Combine like terms: 2 + -9 = -7 -9 + -17k = -7 + -3k Solving -9 + -17k = -7 + -3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3k' to each side of the equation. -9 + -17k + 3k = -7 + -3k + 3k Combine like terms: -17k + 3k = -14k -9 + -14k = -7 + -3k + 3k Combine like terms: -3k + 3k = 0 -9 + -14k = -7 + 0 -9 + -14k = -7 Add '9' to each side of the equation. -9 + 9 + -14k = -7 + 9 Combine like terms: -9 + 9 = 0 0 + -14k = -7 + 9 -14k = -7 + 9 Combine like terms: -7 + 9 = 2 -14k = 2 Divide each side by '-14'. k = -0.1428571429 Simplifying k = -0.1428571429
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