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Simplifying 5(6z + -1) + -2(z + 7) = 16(z + 1) Reorder the terms: 5(-1 + 6z) + -2(z + 7) = 16(z + 1) (-1 * 5 + 6z * 5) + -2(z + 7) = 16(z + 1) (-5 + 30z) + -2(z + 7) = 16(z + 1) Reorder the terms: -5 + 30z + -2(7 + z) = 16(z + 1) -5 + 30z + (7 * -2 + z * -2) = 16(z + 1) -5 + 30z + (-14 + -2z) = 16(z + 1) Reorder the terms: -5 + -14 + 30z + -2z = 16(z + 1) Combine like terms: -5 + -14 = -19 -19 + 30z + -2z = 16(z + 1) Combine like terms: 30z + -2z = 28z -19 + 28z = 16(z + 1) Reorder the terms: -19 + 28z = 16(1 + z) -19 + 28z = (1 * 16 + z * 16) -19 + 28z = (16 + 16z) Solving -19 + 28z = 16 + 16z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-16z' to each side of the equation. -19 + 28z + -16z = 16 + 16z + -16z Combine like terms: 28z + -16z = 12z -19 + 12z = 16 + 16z + -16z Combine like terms: 16z + -16z = 0 -19 + 12z = 16 + 0 -19 + 12z = 16 Add '19' to each side of the equation. -19 + 19 + 12z = 16 + 19 Combine like terms: -19 + 19 = 0 0 + 12z = 16 + 19 12z = 16 + 19 Combine like terms: 16 + 19 = 35 12z = 35 Divide each side by '12'. z = 2.916666667 Simplifying z = 2.916666667
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