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Simplifying 4(k + 2) + 7(k + -3) = 53 Reorder the terms: 4(2 + k) + 7(k + -3) = 53 (2 * 4 + k * 4) + 7(k + -3) = 53 (8 + 4k) + 7(k + -3) = 53 Reorder the terms: 8 + 4k + 7(-3 + k) = 53 8 + 4k + (-3 * 7 + k * 7) = 53 8 + 4k + (-21 + 7k) = 53 Reorder the terms: 8 + -21 + 4k + 7k = 53 Combine like terms: 8 + -21 = -13 -13 + 4k + 7k = 53 Combine like terms: 4k + 7k = 11k -13 + 11k = 53 Solving -13 + 11k = 53 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 11k = 53 + 13 Combine like terms: -13 + 13 = 0 0 + 11k = 53 + 13 11k = 53 + 13 Combine like terms: 53 + 13 = 66 11k = 66 Divide each side by '11'. k = 6 Simplifying k = 6
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