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Simplifying 7(6k + -5) + 7k = 7(5k + -1) Reorder the terms: 7(-5 + 6k) + 7k = 7(5k + -1) (-5 * 7 + 6k * 7) + 7k = 7(5k + -1) (-35 + 42k) + 7k = 7(5k + -1) Combine like terms: 42k + 7k = 49k -35 + 49k = 7(5k + -1) Reorder the terms: -35 + 49k = 7(-1 + 5k) -35 + 49k = (-1 * 7 + 5k * 7) -35 + 49k = (-7 + 35k) Solving -35 + 49k = -7 + 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. -35 + 49k + -35k = -7 + 35k + -35k Combine like terms: 49k + -35k = 14k -35 + 14k = -7 + 35k + -35k Combine like terms: 35k + -35k = 0 -35 + 14k = -7 + 0 -35 + 14k = -7 Add '35' to each side of the equation. -35 + 35 + 14k = -7 + 35 Combine like terms: -35 + 35 = 0 0 + 14k = -7 + 35 14k = -7 + 35 Combine like terms: -7 + 35 = 28 14k = 28 Divide each side by '14'. k = 2 Simplifying k = 2
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