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Simplifying 3(4z + -1) + -2(z + 3) = 5(z + 1) Reorder the terms: 3(-1 + 4z) + -2(z + 3) = 5(z + 1) (-1 * 3 + 4z * 3) + -2(z + 3) = 5(z + 1) (-3 + 12z) + -2(z + 3) = 5(z + 1) Reorder the terms: -3 + 12z + -2(3 + z) = 5(z + 1) -3 + 12z + (3 * -2 + z * -2) = 5(z + 1) -3 + 12z + (-6 + -2z) = 5(z + 1) Reorder the terms: -3 + -6 + 12z + -2z = 5(z + 1) Combine like terms: -3 + -6 = -9 -9 + 12z + -2z = 5(z + 1) Combine like terms: 12z + -2z = 10z -9 + 10z = 5(z + 1) Reorder the terms: -9 + 10z = 5(1 + z) -9 + 10z = (1 * 5 + z * 5) -9 + 10z = (5 + 5z) Solving -9 + 10z = 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. -9 + 10z + -5z = 5 + 5z + -5z Combine like terms: 10z + -5z = 5z -9 + 5z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -9 + 5z = 5 + 0 -9 + 5z = 5 Add '9' to each side of the equation. -9 + 9 + 5z = 5 + 9 Combine like terms: -9 + 9 = 0 0 + 5z = 5 + 9 5z = 5 + 9 Combine like terms: 5 + 9 = 14 5z = 14 Divide each side by '5'. z = 2.8 Simplifying z = 2.8
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