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Simplifying 3(k + -10) + 4(k + -19) = 13 Reorder the terms: 3(-10 + k) + 4(k + -19) = 13 (-10 * 3 + k * 3) + 4(k + -19) = 13 (-30 + 3k) + 4(k + -19) = 13 Reorder the terms: -30 + 3k + 4(-19 + k) = 13 -30 + 3k + (-19 * 4 + k * 4) = 13 -30 + 3k + (-76 + 4k) = 13 Reorder the terms: -30 + -76 + 3k + 4k = 13 Combine like terms: -30 + -76 = -106 -106 + 3k + 4k = 13 Combine like terms: 3k + 4k = 7k -106 + 7k = 13 Solving -106 + 7k = 13 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '106' to each side of the equation. -106 + 106 + 7k = 13 + 106 Combine like terms: -106 + 106 = 0 0 + 7k = 13 + 106 7k = 13 + 106 Combine like terms: 13 + 106 = 119 7k = 119 Divide each side by '7'. k = 17 Simplifying k = 17
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