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Simplifying 1 + -2(k + 4) = 5(6 + -7k) + -4 Reorder the terms: 1 + -2(4 + k) = 5(6 + -7k) + -4 1 + (4 * -2 + k * -2) = 5(6 + -7k) + -4 1 + (-8 + -2k) = 5(6 + -7k) + -4 Combine like terms: 1 + -8 = -7 -7 + -2k = 5(6 + -7k) + -4 -7 + -2k = (6 * 5 + -7k * 5) + -4 -7 + -2k = (30 + -35k) + -4 Reorder the terms: -7 + -2k = 30 + -4 + -35k Combine like terms: 30 + -4 = 26 -7 + -2k = 26 + -35k Solving -7 + -2k = 26 + -35k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '35k' to each side of the equation. -7 + -2k + 35k = 26 + -35k + 35k Combine like terms: -2k + 35k = 33k -7 + 33k = 26 + -35k + 35k Combine like terms: -35k + 35k = 0 -7 + 33k = 26 + 0 -7 + 33k = 26 Add '7' to each side of the equation. -7 + 7 + 33k = 26 + 7 Combine like terms: -7 + 7 = 0 0 + 33k = 26 + 7 33k = 26 + 7 Combine like terms: 26 + 7 = 33 33k = 33 Divide each side by '33'. k = 1 Simplifying k = 1
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