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Simplifying 0.3(4z + 5) + 8.1 = 0.4(4z + -6) Reorder the terms: 0.3(5 + 4z) + 8.1 = 0.4(4z + -6) (5 * 0.3 + 4z * 0.3) + 8.1 = 0.4(4z + -6) (1.5 + 1.2z) + 8.1 = 0.4(4z + -6) Reorder the terms: 1.5 + 8.1 + 1.2z = 0.4(4z + -6) Combine like terms: 1.5 + 8.1 = 9.6 9.6 + 1.2z = 0.4(4z + -6) Reorder the terms: 9.6 + 1.2z = 0.4(-6 + 4z) 9.6 + 1.2z = (-6 * 0.4 + 4z * 0.4) 9.6 + 1.2z = (-2.4 + 1.6z) Solving 9.6 + 1.2z = -2.4 + 1.6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.6z' to each side of the equation. 9.6 + 1.2z + -1.6z = -2.4 + 1.6z + -1.6z Combine like terms: 1.2z + -1.6z = -0.4z 9.6 + -0.4z = -2.4 + 1.6z + -1.6z Combine like terms: 1.6z + -1.6z = 0.0 9.6 + -0.4z = -2.4 + 0.0 9.6 + -0.4z = -2.4 Add '-9.6' to each side of the equation. 9.6 + -9.6 + -0.4z = -2.4 + -9.6 Combine like terms: 9.6 + -9.6 = 0.0 0.0 + -0.4z = -2.4 + -9.6 -0.4z = -2.4 + -9.6 Combine like terms: -2.4 + -9.6 = -12 -0.4z = -12 Divide each side by '-0.4'. z = 30 Simplifying z = 30
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