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Simplifying 3(2k + -7) + -3(5k + 2) = 4 + -2(k + 3) Reorder the terms: 3(-7 + 2k) + -3(5k + 2) = 4 + -2(k + 3) (-7 * 3 + 2k * 3) + -3(5k + 2) = 4 + -2(k + 3) (-21 + 6k) + -3(5k + 2) = 4 + -2(k + 3) Reorder the terms: -21 + 6k + -3(2 + 5k) = 4 + -2(k + 3) -21 + 6k + (2 * -3 + 5k * -3) = 4 + -2(k + 3) -21 + 6k + (-6 + -15k) = 4 + -2(k + 3) Reorder the terms: -21 + -6 + 6k + -15k = 4 + -2(k + 3) Combine like terms: -21 + -6 = -27 -27 + 6k + -15k = 4 + -2(k + 3) Combine like terms: 6k + -15k = -9k -27 + -9k = 4 + -2(k + 3) Reorder the terms: -27 + -9k = 4 + -2(3 + k) -27 + -9k = 4 + (3 * -2 + k * -2) -27 + -9k = 4 + (-6 + -2k) Combine like terms: 4 + -6 = -2 -27 + -9k = -2 + -2k Solving -27 + -9k = -2 + -2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2k' to each side of the equation. -27 + -9k + 2k = -2 + -2k + 2k Combine like terms: -9k + 2k = -7k -27 + -7k = -2 + -2k + 2k Combine like terms: -2k + 2k = 0 -27 + -7k = -2 + 0 -27 + -7k = -2 Add '27' to each side of the equation. -27 + 27 + -7k = -2 + 27 Combine like terms: -27 + 27 = 0 0 + -7k = -2 + 27 -7k = -2 + 27 Combine like terms: -2 + 27 = 25 -7k = 25 Divide each side by '-7'. k = -3.571428571 Simplifying k = -3.571428571
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