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Simplifying 3(2p + -7) + -5(5p + 2) = 4 + -3(p + 1) Reorder the terms: 3(-7 + 2p) + -5(5p + 2) = 4 + -3(p + 1) (-7 * 3 + 2p * 3) + -5(5p + 2) = 4 + -3(p + 1) (-21 + 6p) + -5(5p + 2) = 4 + -3(p + 1) Reorder the terms: -21 + 6p + -5(2 + 5p) = 4 + -3(p + 1) -21 + 6p + (2 * -5 + 5p * -5) = 4 + -3(p + 1) -21 + 6p + (-10 + -25p) = 4 + -3(p + 1) Reorder the terms: -21 + -10 + 6p + -25p = 4 + -3(p + 1) Combine like terms: -21 + -10 = -31 -31 + 6p + -25p = 4 + -3(p + 1) Combine like terms: 6p + -25p = -19p -31 + -19p = 4 + -3(p + 1) Reorder the terms: -31 + -19p = 4 + -3(1 + p) -31 + -19p = 4 + (1 * -3 + p * -3) -31 + -19p = 4 + (-3 + -3p) Combine like terms: 4 + -3 = 1 -31 + -19p = 1 + -3p Solving -31 + -19p = 1 + -3p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3p' to each side of the equation. -31 + -19p + 3p = 1 + -3p + 3p Combine like terms: -19p + 3p = -16p -31 + -16p = 1 + -3p + 3p Combine like terms: -3p + 3p = 0 -31 + -16p = 1 + 0 -31 + -16p = 1 Add '31' to each side of the equation. -31 + 31 + -16p = 1 + 31 Combine like terms: -31 + 31 = 0 0 + -16p = 1 + 31 -16p = 1 + 31 Combine like terms: 1 + 31 = 32 -16p = 32 Divide each side by '-16'. p = -2 Simplifying p = -2
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