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Simplifying 2[(3 + k) + -7] = 3[(3 + -1k) + -1(-2)] Remove parenthesis around (3 + k) 2[3 + k + -7] = 3[(3 + -1k) + -1(-2)] Reorder the terms: 2[3 + -7 + k] = 3[(3 + -1k) + -1(-2)] Combine like terms: 3 + -7 = -4 2[-4 + k] = 3[(3 + -1k) + -1(-2)] [-4 * 2 + k * 2] = 3[(3 + -1k) + -1(-2)] [-8 + 2k] = 3[(3 + -1k) + -1(-2)] Remove parenthesis around (3 + -1k) -8 + 2k = 3[3 + -1k + -1(-2)] Multiply -1 * -2 -8 + 2k = 3[3 + -1k + 2] Reorder the terms: -8 + 2k = 3[3 + 2 + -1k] Combine like terms: 3 + 2 = 5 -8 + 2k = 3[5 + -1k] -8 + 2k = [5 * 3 + -1k * 3] -8 + 2k = [15 + -3k] Solving -8 + 2k = 15 + -3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3k' to each side of the equation. -8 + 2k + 3k = 15 + -3k + 3k Combine like terms: 2k + 3k = 5k -8 + 5k = 15 + -3k + 3k Combine like terms: -3k + 3k = 0 -8 + 5k = 15 + 0 -8 + 5k = 15 Add '8' to each side of the equation. -8 + 8 + 5k = 15 + 8 Combine like terms: -8 + 8 = 0 0 + 5k = 15 + 8 5k = 15 + 8 Combine like terms: 15 + 8 = 23 5k = 23 Divide each side by '5'. k = 4.6 Simplifying k = 4.6
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