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Simplifying 3(6z + -1) + -5(z + 5) = 5(z + 1) Reorder the terms: 3(-1 + 6z) + -5(z + 5) = 5(z + 1) (-1 * 3 + 6z * 3) + -5(z + 5) = 5(z + 1) (-3 + 18z) + -5(z + 5) = 5(z + 1) Reorder the terms: -3 + 18z + -5(5 + z) = 5(z + 1) -3 + 18z + (5 * -5 + z * -5) = 5(z + 1) -3 + 18z + (-25 + -5z) = 5(z + 1) Reorder the terms: -3 + -25 + 18z + -5z = 5(z + 1) Combine like terms: -3 + -25 = -28 -28 + 18z + -5z = 5(z + 1) Combine like terms: 18z + -5z = 13z -28 + 13z = 5(z + 1) Reorder the terms: -28 + 13z = 5(1 + z) -28 + 13z = (1 * 5 + z * 5) -28 + 13z = (5 + 5z) Solving -28 + 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. -28 + 13z + -5z = 5 + 5z + -5z Combine like terms: 13z + -5z = 8z -28 + 8z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -28 + 8z = 5 + 0 -28 + 8z = 5 Add '28' to each side of the equation. -28 + 28 + 8z = 5 + 28 Combine like terms: -28 + 28 = 0 0 + 8z = 5 + 28 8z = 5 + 28 Combine like terms: 5 + 28 = 33 8z = 33 Divide each side by '8'. z = 4.125 Simplifying z = 4.125
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