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Simplifying 0.3(3z + 6) + 6.7 = 0.7(3z + -5) Reorder the terms: 0.3(6 + 3z) + 6.7 = 0.7(3z + -5) (6 * 0.3 + 3z * 0.3) + 6.7 = 0.7(3z + -5) (1.8 + 0.9z) + 6.7 = 0.7(3z + -5) Reorder the terms: 1.8 + 6.7 + 0.9z = 0.7(3z + -5) Combine like terms: 1.8 + 6.7 = 8.5 8.5 + 0.9z = 0.7(3z + -5) Reorder the terms: 8.5 + 0.9z = 0.7(-5 + 3z) 8.5 + 0.9z = (-5 * 0.7 + 3z * 0.7) 8.5 + 0.9z = (-3.5 + 2.1z) Solving 8.5 + 0.9z = -3.5 + 2.1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.1z' to each side of the equation. 8.5 + 0.9z + -2.1z = -3.5 + 2.1z + -2.1z Combine like terms: 0.9z + -2.1z = -1.2z 8.5 + -1.2z = -3.5 + 2.1z + -2.1z Combine like terms: 2.1z + -2.1z = 0.0 8.5 + -1.2z = -3.5 + 0.0 8.5 + -1.2z = -3.5 Add '-8.5' to each side of the equation. 8.5 + -8.5 + -1.2z = -3.5 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -1.2z = -3.5 + -8.5 -1.2z = -3.5 + -8.5 Combine like terms: -3.5 + -8.5 = -12 -1.2z = -12 Divide each side by '-1.2'. z = 10 Simplifying z = 10
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