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Simplifying 6(3z + -1) + -5(z + 2) = 6(z + 1) Reorder the terms: 6(-1 + 3z) + -5(z + 2) = 6(z + 1) (-1 * 6 + 3z * 6) + -5(z + 2) = 6(z + 1) (-6 + 18z) + -5(z + 2) = 6(z + 1) Reorder the terms: -6 + 18z + -5(2 + z) = 6(z + 1) -6 + 18z + (2 * -5 + z * -5) = 6(z + 1) -6 + 18z + (-10 + -5z) = 6(z + 1) Reorder the terms: -6 + -10 + 18z + -5z = 6(z + 1) Combine like terms: -6 + -10 = -16 -16 + 18z + -5z = 6(z + 1) Combine like terms: 18z + -5z = 13z -16 + 13z = 6(z + 1) Reorder the terms: -16 + 13z = 6(1 + z) -16 + 13z = (1 * 6 + z * 6) -16 + 13z = (6 + 6z) Solving -16 + 13z = 6 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -16 + 13z + -6z = 6 + 6z + -6z Combine like terms: 13z + -6z = 7z -16 + 7z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -16 + 7z = 6 + 0 -16 + 7z = 6 Add '16' to each side of the equation. -16 + 16 + 7z = 6 + 16 Combine like terms: -16 + 16 = 0 0 + 7z = 6 + 16 7z = 6 + 16 Combine like terms: 6 + 16 = 22 7z = 22 Divide each side by '7'. z = 3.142857143 Simplifying z = 3.142857143
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