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Simplifying (10p + -15) + -1(2k + -2) = (2k + -2) + -1(2p + 3) Reorder the terms: (-15 + 10p) + -1(2k + -2) = (2k + -2) + -1(2p + 3) Remove parenthesis around (-15 + 10p) -15 + 10p + -1(2k + -2) = (2k + -2) + -1(2p + 3) Reorder the terms: -15 + 10p + -1(-2 + 2k) = (2k + -2) + -1(2p + 3) -15 + 10p + (-2 * -1 + 2k * -1) = (2k + -2) + -1(2p + 3) -15 + 10p + (2 + -2k) = (2k + -2) + -1(2p + 3) Reorder the terms: -15 + 2 + -2k + 10p = (2k + -2) + -1(2p + 3) Combine like terms: -15 + 2 = -13 -13 + -2k + 10p = (2k + -2) + -1(2p + 3) Reorder the terms: -13 + -2k + 10p = (-2 + 2k) + -1(2p + 3) Remove parenthesis around (-2 + 2k) -13 + -2k + 10p = -2 + 2k + -1(2p + 3) Reorder the terms: -13 + -2k + 10p = -2 + 2k + -1(3 + 2p) -13 + -2k + 10p = -2 + 2k + (3 * -1 + 2p * -1) -13 + -2k + 10p = -2 + 2k + (-3 + -2p) Reorder the terms: -13 + -2k + 10p = -2 + -3 + 2k + -2p Combine like terms: -2 + -3 = -5 -13 + -2k + 10p = -5 + 2k + -2p Solving -13 + -2k + 10p = -5 + 2k + -2p 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. -13 + -2k + -2k + 10p = -5 + 2k + -2k + -2p Combine like terms: -2k + -2k = -4k -13 + -4k + 10p = -5 + 2k + -2k + -2p Combine like terms: 2k + -2k = 0 -13 + -4k + 10p = -5 + 0 + -2p -13 + -4k + 10p = -5 + -2p Add '13' to each side of the equation. -13 + -4k + 13 + 10p = -5 + 13 + -2p Reorder the terms: -13 + 13 + -4k + 10p = -5 + 13 + -2p Combine like terms: -13 + 13 = 0 0 + -4k + 10p = -5 + 13 + -2p -4k + 10p = -5 + 13 + -2p Combine like terms: -5 + 13 = 8 -4k + 10p = 8 + -2p Add '-10p' to each side of the equation. -4k + 10p + -10p = 8 + -2p + -10p Combine like terms: 10p + -10p = 0 -4k + 0 = 8 + -2p + -10p -4k = 8 + -2p + -10p Combine like terms: -2p + -10p = -12p -4k = 8 + -12p Divide each side by '-4'. k = -2 + 3p Simplifying k = -2 + 3p
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