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Simplifying -43 = -7(k + -5) + -2(7k + -3) Reorder the terms: -43 = -7(-5 + k) + -2(7k + -3) -43 = (-5 * -7 + k * -7) + -2(7k + -3) -43 = (35 + -7k) + -2(7k + -3) Reorder the terms: -43 = 35 + -7k + -2(-3 + 7k) -43 = 35 + -7k + (-3 * -2 + 7k * -2) -43 = 35 + -7k + (6 + -14k) Reorder the terms: -43 = 35 + 6 + -7k + -14k Combine like terms: 35 + 6 = 41 -43 = 41 + -7k + -14k Combine like terms: -7k + -14k = -21k -43 = 41 + -21k Solving -43 = 41 + -21k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '21k' to each side of the equation. -43 + 21k = 41 + -21k + 21k Combine like terms: -21k + 21k = 0 -43 + 21k = 41 + 0 -43 + 21k = 41 Add '43' to each side of the equation. -43 + 43 + 21k = 41 + 43 Combine like terms: -43 + 43 = 0 0 + 21k = 41 + 43 21k = 41 + 43 Combine like terms: 41 + 43 = 84 21k = 84 Divide each side by '21'. k = 4 Simplifying k = 4
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