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Simplifying -7(1 + -7k) = 7(-11 + 5k) (1 * -7 + -7k * -7) = 7(-11 + 5k) (-7 + 49k) = 7(-11 + 5k) -7 + 49k = (-11 * 7 + 5k * 7) -7 + 49k = (-77 + 35k) Solving -7 + 49k = -77 + 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 + 49k + -35k = -77 + 35k + -35k Combine like terms: 49k + -35k = 14k -7 + 14k = -77 + 35k + -35k Combine like terms: 35k + -35k = 0 -7 + 14k = -77 + 0 -7 + 14k = -77 Add '7' to each side of the equation. -7 + 7 + 14k = -77 + 7 Combine like terms: -7 + 7 = 0 0 + 14k = -77 + 7 14k = -77 + 7 Combine like terms: -77 + 7 = -70 14k = -70 Divide each side by '14'. k = -5 Simplifying k = -5
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