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Simplifying 12 + 2k = -7(-5k + 4) + 7 Reorder the terms: 12 + 2k = -7(4 + -5k) + 7 12 + 2k = (4 * -7 + -5k * -7) + 7 12 + 2k = (-28 + 35k) + 7 Reorder the terms: 12 + 2k = -28 + 7 + 35k Combine like terms: -28 + 7 = -21 12 + 2k = -21 + 35k Solving 12 + 2k = -21 + 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. 12 + 2k + -35k = -21 + 35k + -35k Combine like terms: 2k + -35k = -33k 12 + -33k = -21 + 35k + -35k Combine like terms: 35k + -35k = 0 12 + -33k = -21 + 0 12 + -33k = -21 Add '-12' to each side of the equation. 12 + -12 + -33k = -21 + -12 Combine like terms: 12 + -12 = 0 0 + -33k = -21 + -12 -33k = -21 + -12 Combine like terms: -21 + -12 = -33 -33k = -33 Divide each side by '-33'. k = 1 Simplifying k = 1
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