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Simplifying 3(2k + -5) + -5(5k + 3) = 4 + -2(k + 1) Reorder the terms: 3(-5 + 2k) + -5(5k + 3) = 4 + -2(k + 1) (-5 * 3 + 2k * 3) + -5(5k + 3) = 4 + -2(k + 1) (-15 + 6k) + -5(5k + 3) = 4 + -2(k + 1) Reorder the terms: -15 + 6k + -5(3 + 5k) = 4 + -2(k + 1) -15 + 6k + (3 * -5 + 5k * -5) = 4 + -2(k + 1) -15 + 6k + (-15 + -25k) = 4 + -2(k + 1) Reorder the terms: -15 + -15 + 6k + -25k = 4 + -2(k + 1) Combine like terms: -15 + -15 = -30 -30 + 6k + -25k = 4 + -2(k + 1) Combine like terms: 6k + -25k = -19k -30 + -19k = 4 + -2(k + 1) Reorder the terms: -30 + -19k = 4 + -2(1 + k) -30 + -19k = 4 + (1 * -2 + k * -2) -30 + -19k = 4 + (-2 + -2k) Combine like terms: 4 + -2 = 2 -30 + -19k = 2 + -2k Solving -30 + -19k = 2 + -2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2k' to each side of the equation. -30 + -19k + 2k = 2 + -2k + 2k Combine like terms: -19k + 2k = -17k -30 + -17k = 2 + -2k + 2k Combine like terms: -2k + 2k = 0 -30 + -17k = 2 + 0 -30 + -17k = 2 Add '30' to each side of the equation. -30 + 30 + -17k = 2 + 30 Combine like terms: -30 + 30 = 0 0 + -17k = 2 + 30 -17k = 2 + 30 Combine like terms: 2 + 30 = 32 -17k = 32 Divide each side by '-17'. k = -1.882352941 Simplifying k = -1.882352941
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