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