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Simplifying 3(6z + -1) + -5(z + 3) = 5(z + 1) Reorder the terms: 3(-1 + 6z) + -5(z + 3) = 5(z + 1) (-1 * 3 + 6z * 3) + -5(z + 3) = 5(z + 1) (-3 + 18z) + -5(z + 3) = 5(z + 1) Reorder the terms: -3 + 18z + -5(3 + z) = 5(z + 1) -3 + 18z + (3 * -5 + z * -5) = 5(z + 1) -3 + 18z + (-15 + -5z) = 5(z + 1) Reorder the terms: -3 + -15 + 18z + -5z = 5(z + 1) Combine like terms: -3 + -15 = -18 -18 + 18z + -5z = 5(z + 1) Combine like terms: 18z + -5z = 13z -18 + 13z = 5(z + 1) Reorder the terms: -18 + 13z = 5(1 + z) -18 + 13z = (1 * 5 + z * 5) -18 + 13z = (5 + 5z) Solving -18 + 13z = 5 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -18 + 13z + -5z = 5 + 5z + -5z Combine like terms: 13z + -5z = 8z -18 + 8z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -18 + 8z = 5 + 0 -18 + 8z = 5 Add '18' to each side of the equation. -18 + 18 + 8z = 5 + 18 Combine like terms: -18 + 18 = 0 0 + 8z = 5 + 18 8z = 5 + 18 Combine like terms: 5 + 18 = 23 8z = 23 Divide each side by '8'. z = 2.875 Simplifying z = 2.875
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