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Simplifying 3(6z + -1) + -5(z + 9) = 7(z + 1) Reorder the terms: 3(-1 + 6z) + -5(z + 9) = 7(z + 1) (-1 * 3 + 6z * 3) + -5(z + 9) = 7(z + 1) (-3 + 18z) + -5(z + 9) = 7(z + 1) Reorder the terms: -3 + 18z + -5(9 + z) = 7(z + 1) -3 + 18z + (9 * -5 + z * -5) = 7(z + 1) -3 + 18z + (-45 + -5z) = 7(z + 1) Reorder the terms: -3 + -45 + 18z + -5z = 7(z + 1) Combine like terms: -3 + -45 = -48 -48 + 18z + -5z = 7(z + 1) Combine like terms: 18z + -5z = 13z -48 + 13z = 7(z + 1) Reorder the terms: -48 + 13z = 7(1 + z) -48 + 13z = (1 * 7 + z * 7) -48 + 13z = (7 + 7z) Solving -48 + 13z = 7 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. -48 + 13z + -7z = 7 + 7z + -7z Combine like terms: 13z + -7z = 6z -48 + 6z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -48 + 6z = 7 + 0 -48 + 6z = 7 Add '48' to each side of the equation. -48 + 48 + 6z = 7 + 48 Combine like terms: -48 + 48 = 0 0 + 6z = 7 + 48 6z = 7 + 48 Combine like terms: 7 + 48 = 55 6z = 55 Divide each side by '6'. z = 9.166666667 Simplifying z = 9.166666667
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