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Simplifying 0.3(3z + 6) + 7.8 = 0.4(3z + -6) Reorder the terms: 0.3(6 + 3z) + 7.8 = 0.4(3z + -6) (6 * 0.3 + 3z * 0.3) + 7.8 = 0.4(3z + -6) (1.8 + 0.9z) + 7.8 = 0.4(3z + -6) Reorder the terms: 1.8 + 7.8 + 0.9z = 0.4(3z + -6) Combine like terms: 1.8 + 7.8 = 9.6 9.6 + 0.9z = 0.4(3z + -6) Reorder the terms: 9.6 + 0.9z = 0.4(-6 + 3z) 9.6 + 0.9z = (-6 * 0.4 + 3z * 0.4) 9.6 + 0.9z = (-2.4 + 1.2z) Solving 9.6 + 0.9z = -2.4 + 1.2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.2z' to each side of the equation. 9.6 + 0.9z + -1.2z = -2.4 + 1.2z + -1.2z Combine like terms: 0.9z + -1.2z = -0.3z 9.6 + -0.3z = -2.4 + 1.2z + -1.2z Combine like terms: 1.2z + -1.2z = 0.0 9.6 + -0.3z = -2.4 + 0.0 9.6 + -0.3z = -2.4 Add '-9.6' to each side of the equation. 9.6 + -9.6 + -0.3z = -2.4 + -9.6 Combine like terms: 9.6 + -9.6 = 0.0 0.0 + -0.3z = -2.4 + -9.6 -0.3z = -2.4 + -9.6 Combine like terms: -2.4 + -9.6 = -12 -0.3z = -12 Divide each side by '-0.3'. z = 40 Simplifying z = 40
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