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Simplifying 2(6z + -1) + -3(z + 4) = 5(z + 1) Reorder the terms: 2(-1 + 6z) + -3(z + 4) = 5(z + 1) (-1 * 2 + 6z * 2) + -3(z + 4) = 5(z + 1) (-2 + 12z) + -3(z + 4) = 5(z + 1) Reorder the terms: -2 + 12z + -3(4 + z) = 5(z + 1) -2 + 12z + (4 * -3 + z * -3) = 5(z + 1) -2 + 12z + (-12 + -3z) = 5(z + 1) Reorder the terms: -2 + -12 + 12z + -3z = 5(z + 1) Combine like terms: -2 + -12 = -14 -14 + 12z + -3z = 5(z + 1) Combine like terms: 12z + -3z = 9z -14 + 9z = 5(z + 1) Reorder the terms: -14 + 9z = 5(1 + z) -14 + 9z = (1 * 5 + z * 5) -14 + 9z = (5 + 5z) Solving -14 + 9z = 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. -14 + 9z + -5z = 5 + 5z + -5z Combine like terms: 9z + -5z = 4z -14 + 4z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -14 + 4z = 5 + 0 -14 + 4z = 5 Add '14' to each side of the equation. -14 + 14 + 4z = 5 + 14 Combine like terms: -14 + 14 = 0 0 + 4z = 5 + 14 4z = 5 + 14 Combine like terms: 5 + 14 = 19 4z = 19 Divide each side by '4'. z = 4.75 Simplifying z = 4.75
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