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Simplifying -75 = 3(k + -7) + -6(3k + 4) Reorder the terms: -75 = 3(-7 + k) + -6(3k + 4) -75 = (-7 * 3 + k * 3) + -6(3k + 4) -75 = (-21 + 3k) + -6(3k + 4) Reorder the terms: -75 = -21 + 3k + -6(4 + 3k) -75 = -21 + 3k + (4 * -6 + 3k * -6) -75 = -21 + 3k + (-24 + -18k) Reorder the terms: -75 = -21 + -24 + 3k + -18k Combine like terms: -21 + -24 = -45 -75 = -45 + 3k + -18k Combine like terms: 3k + -18k = -15k -75 = -45 + -15k Solving -75 = -45 + -15k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '15k' to each side of the equation. -75 + 15k = -45 + -15k + 15k Combine like terms: -15k + 15k = 0 -75 + 15k = -45 + 0 -75 + 15k = -45 Add '75' to each side of the equation. -75 + 75 + 15k = -45 + 75 Combine like terms: -75 + 75 = 0 0 + 15k = -45 + 75 15k = -45 + 75 Combine like terms: -45 + 75 = 30 15k = 30 Divide each side by '15'. k = 2 Simplifying k = 2
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