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Simplifying 5(6z + -1) + -2(z + 7) = 12(z + 1) Reorder the terms: 5(-1 + 6z) + -2(z + 7) = 12(z + 1) (-1 * 5 + 6z * 5) + -2(z + 7) = 12(z + 1) (-5 + 30z) + -2(z + 7) = 12(z + 1) Reorder the terms: -5 + 30z + -2(7 + z) = 12(z + 1) -5 + 30z + (7 * -2 + z * -2) = 12(z + 1) -5 + 30z + (-14 + -2z) = 12(z + 1) Reorder the terms: -5 + -14 + 30z + -2z = 12(z + 1) Combine like terms: -5 + -14 = -19 -19 + 30z + -2z = 12(z + 1) Combine like terms: 30z + -2z = 28z -19 + 28z = 12(z + 1) Reorder the terms: -19 + 28z = 12(1 + z) -19 + 28z = (1 * 12 + z * 12) -19 + 28z = (12 + 12z) Solving -19 + 28z = 12 + 12z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-12z' to each side of the equation. -19 + 28z + -12z = 12 + 12z + -12z Combine like terms: 28z + -12z = 16z -19 + 16z = 12 + 12z + -12z Combine like terms: 12z + -12z = 0 -19 + 16z = 12 + 0 -19 + 16z = 12 Add '19' to each side of the equation. -19 + 19 + 16z = 12 + 19 Combine like terms: -19 + 19 = 0 0 + 16z = 12 + 19 16z = 12 + 19 Combine like terms: 12 + 19 = 31 16z = 31 Divide each side by '16'. z = 1.9375 Simplifying z = 1.9375
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