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Simplifying 13 + 2k = 3k + 4(k + -3) Reorder the terms: 13 + 2k = 3k + 4(-3 + k) 13 + 2k = 3k + (-3 * 4 + k * 4) 13 + 2k = 3k + (-12 + 4k) Reorder the terms: 13 + 2k = -12 + 3k + 4k Combine like terms: 3k + 4k = 7k 13 + 2k = -12 + 7k Solving 13 + 2k = -12 + 7k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7k' to each side of the equation. 13 + 2k + -7k = -12 + 7k + -7k Combine like terms: 2k + -7k = -5k 13 + -5k = -12 + 7k + -7k Combine like terms: 7k + -7k = 0 13 + -5k = -12 + 0 13 + -5k = -12 Add '-13' to each side of the equation. 13 + -13 + -5k = -12 + -13 Combine like terms: 13 + -13 = 0 0 + -5k = -12 + -13 -5k = -12 + -13 Combine like terms: -12 + -13 = -25 -5k = -25 Divide each side by '-5'. k = 5 Simplifying k = 5
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