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Simplifying 5[(2k + 1) + -3(k + -3)] = 2(k + -10) + 7 Reorder the terms: 5[(1 + 2k) + -3(k + -3)] = 2(k + -10) + 7 Remove parenthesis around (1 + 2k) 5[1 + 2k + -3(k + -3)] = 2(k + -10) + 7 Reorder the terms: 5[1 + 2k + -3(-3 + k)] = 2(k + -10) + 7 5[1 + 2k + (-3 * -3 + k * -3)] = 2(k + -10) + 7 5[1 + 2k + (9 + -3k)] = 2(k + -10) + 7 Reorder the terms: 5[1 + 9 + 2k + -3k] = 2(k + -10) + 7 Combine like terms: 1 + 9 = 10 5[10 + 2k + -3k] = 2(k + -10) + 7 Combine like terms: 2k + -3k = -1k 5[10 + -1k] = 2(k + -10) + 7 [10 * 5 + -1k * 5] = 2(k + -10) + 7 [50 + -5k] = 2(k + -10) + 7 Reorder the terms: 50 + -5k = 2(-10 + k) + 7 50 + -5k = (-10 * 2 + k * 2) + 7 50 + -5k = (-20 + 2k) + 7 Reorder the terms: 50 + -5k = -20 + 7 + 2k Combine like terms: -20 + 7 = -13 50 + -5k = -13 + 2k Solving 50 + -5k = -13 + 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. 50 + -5k + -2k = -13 + 2k + -2k Combine like terms: -5k + -2k = -7k 50 + -7k = -13 + 2k + -2k Combine like terms: 2k + -2k = 0 50 + -7k = -13 + 0 50 + -7k = -13 Add '-50' to each side of the equation. 50 + -50 + -7k = -13 + -50 Combine like terms: 50 + -50 = 0 0 + -7k = -13 + -50 -7k = -13 + -50 Combine like terms: -13 + -50 = -63 -7k = -63 Divide each side by '-7'. k = 9 Simplifying k = 9
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