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Simplifying 5(3z + -1) + -2(z + 6) = 6(z + 1) Reorder the terms: 5(-1 + 3z) + -2(z + 6) = 6(z + 1) (-1 * 5 + 3z * 5) + -2(z + 6) = 6(z + 1) (-5 + 15z) + -2(z + 6) = 6(z + 1) Reorder the terms: -5 + 15z + -2(6 + z) = 6(z + 1) -5 + 15z + (6 * -2 + z * -2) = 6(z + 1) -5 + 15z + (-12 + -2z) = 6(z + 1) Reorder the terms: -5 + -12 + 15z + -2z = 6(z + 1) Combine like terms: -5 + -12 = -17 -17 + 15z + -2z = 6(z + 1) Combine like terms: 15z + -2z = 13z -17 + 13z = 6(z + 1) Reorder the terms: -17 + 13z = 6(1 + z) -17 + 13z = (1 * 6 + z * 6) -17 + 13z = (6 + 6z) Solving -17 + 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. -17 + 13z + -6z = 6 + 6z + -6z Combine like terms: 13z + -6z = 7z -17 + 7z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -17 + 7z = 6 + 0 -17 + 7z = 6 Add '17' to each side of the equation. -17 + 17 + 7z = 6 + 17 Combine like terms: -17 + 17 = 0 0 + 7z = 6 + 17 7z = 6 + 17 Combine like terms: 6 + 17 = 23 7z = 23 Divide each side by '7'. z = 3.285714286 Simplifying z = 3.285714286
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