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Simplifying 3(6z + -1) + -2(z + 5) = 12(z + 1) Reorder the terms: 3(-1 + 6z) + -2(z + 5) = 12(z + 1) (-1 * 3 + 6z * 3) + -2(z + 5) = 12(z + 1) (-3 + 18z) + -2(z + 5) = 12(z + 1) Reorder the terms: -3 + 18z + -2(5 + z) = 12(z + 1) -3 + 18z + (5 * -2 + z * -2) = 12(z + 1) -3 + 18z + (-10 + -2z) = 12(z + 1) Reorder the terms: -3 + -10 + 18z + -2z = 12(z + 1) Combine like terms: -3 + -10 = -13 -13 + 18z + -2z = 12(z + 1) Combine like terms: 18z + -2z = 16z -13 + 16z = 12(z + 1) Reorder the terms: -13 + 16z = 12(1 + z) -13 + 16z = (1 * 12 + z * 12) -13 + 16z = (12 + 12z) Solving -13 + 16z = 12 + 12z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-12z' to each side of the equation. -13 + 16z + -12z = 12 + 12z + -12z Combine like terms: 16z + -12z = 4z -13 + 4z = 12 + 12z + -12z Combine like terms: 12z + -12z = 0 -13 + 4z = 12 + 0 -13 + 4z = 12 Add '13' to each side of the equation. -13 + 13 + 4z = 12 + 13 Combine like terms: -13 + 13 = 0 0 + 4z = 12 + 13 4z = 12 + 13 Combine like terms: 12 + 13 = 25 4z = 25 Divide each side by '4'. z = 6.25 Simplifying z = 6.25
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