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Simplifying 5(3z + -1) + -3(z + 6) = 4(z + 1) Reorder the terms: 5(-1 + 3z) + -3(z + 6) = 4(z + 1) (-1 * 5 + 3z * 5) + -3(z + 6) = 4(z + 1) (-5 + 15z) + -3(z + 6) = 4(z + 1) Reorder the terms: -5 + 15z + -3(6 + z) = 4(z + 1) -5 + 15z + (6 * -3 + z * -3) = 4(z + 1) -5 + 15z + (-18 + -3z) = 4(z + 1) Reorder the terms: -5 + -18 + 15z + -3z = 4(z + 1) Combine like terms: -5 + -18 = -23 -23 + 15z + -3z = 4(z + 1) Combine like terms: 15z + -3z = 12z -23 + 12z = 4(z + 1) Reorder the terms: -23 + 12z = 4(1 + z) -23 + 12z = (1 * 4 + z * 4) -23 + 12z = (4 + 4z) Solving -23 + 12z = 4 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -23 + 12z + -4z = 4 + 4z + -4z Combine like terms: 12z + -4z = 8z -23 + 8z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -23 + 8z = 4 + 0 -23 + 8z = 4 Add '23' to each side of the equation. -23 + 23 + 8z = 4 + 23 Combine like terms: -23 + 23 = 0 0 + 8z = 4 + 23 8z = 4 + 23 Combine like terms: 4 + 23 = 27 8z = 27 Divide each side by '8'. z = 3.375 Simplifying z = 3.375
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