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Simplifying 1 + -1(2z + -3) + 6 = 3(z + 4) Reorder the terms: 1 + -1(-3 + 2z) + 6 = 3(z + 4) 1 + (-3 * -1 + 2z * -1) + 6 = 3(z + 4) 1 + (3 + -2z) + 6 = 3(z + 4) Reorder the terms: 1 + 3 + 6 + -2z = 3(z + 4) Combine like terms: 1 + 3 = 4 4 + 6 + -2z = 3(z + 4) Combine like terms: 4 + 6 = 10 10 + -2z = 3(z + 4) Reorder the terms: 10 + -2z = 3(4 + z) 10 + -2z = (4 * 3 + z * 3) 10 + -2z = (12 + 3z) Solving 10 + -2z = 12 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. 10 + -2z + -3z = 12 + 3z + -3z Combine like terms: -2z + -3z = -5z 10 + -5z = 12 + 3z + -3z Combine like terms: 3z + -3z = 0 10 + -5z = 12 + 0 10 + -5z = 12 Add '-10' to each side of the equation. 10 + -10 + -5z = 12 + -10 Combine like terms: 10 + -10 = 0 0 + -5z = 12 + -10 -5z = 12 + -10 Combine like terms: 12 + -10 = 2 -5z = 2 Divide each side by '-5'. z = -0.4 Simplifying z = -0.4
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