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Simplifying -7[(6p + 3) + -1(4p + -7)] = 2(5 + -1p) + -8 Reorder the terms: -7[(3 + 6p) + -1(4p + -7)] = 2(5 + -1p) + -8 Remove parenthesis around (3 + 6p) -7[3 + 6p + -1(4p + -7)] = 2(5 + -1p) + -8 Reorder the terms: -7[3 + 6p + -1(-7 + 4p)] = 2(5 + -1p) + -8 -7[3 + 6p + (-7 * -1 + 4p * -1)] = 2(5 + -1p) + -8 -7[3 + 6p + (7 + -4p)] = 2(5 + -1p) + -8 Reorder the terms: -7[3 + 7 + 6p + -4p] = 2(5 + -1p) + -8 Combine like terms: 3 + 7 = 10 -7[10 + 6p + -4p] = 2(5 + -1p) + -8 Combine like terms: 6p + -4p = 2p -7[10 + 2p] = 2(5 + -1p) + -8 [10 * -7 + 2p * -7] = 2(5 + -1p) + -8 [-70 + -14p] = 2(5 + -1p) + -8 -70 + -14p = (5 * 2 + -1p * 2) + -8 -70 + -14p = (10 + -2p) + -8 Reorder the terms: -70 + -14p = 10 + -8 + -2p Combine like terms: 10 + -8 = 2 -70 + -14p = 2 + -2p Solving -70 + -14p = 2 + -2p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2p' to each side of the equation. -70 + -14p + 2p = 2 + -2p + 2p Combine like terms: -14p + 2p = -12p -70 + -12p = 2 + -2p + 2p Combine like terms: -2p + 2p = 0 -70 + -12p = 2 + 0 -70 + -12p = 2 Add '70' to each side of the equation. -70 + 70 + -12p = 2 + 70 Combine like terms: -70 + 70 = 0 0 + -12p = 2 + 70 -12p = 2 + 70 Combine like terms: 2 + 70 = 72 -12p = 72 Divide each side by '-12'. p = -6 Simplifying p = -6
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