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Simplifying 0.3(4z + 6) + 3.8 = 0.4(4z + -6) Reorder the terms: 0.3(6 + 4z) + 3.8 = 0.4(4z + -6) (6 * 0.3 + 4z * 0.3) + 3.8 = 0.4(4z + -6) (1.8 + 1.2z) + 3.8 = 0.4(4z + -6) Reorder the terms: 1.8 + 3.8 + 1.2z = 0.4(4z + -6) Combine like terms: 1.8 + 3.8 = 5.6 5.6 + 1.2z = 0.4(4z + -6) Reorder the terms: 5.6 + 1.2z = 0.4(-6 + 4z) 5.6 + 1.2z = (-6 * 0.4 + 4z * 0.4) 5.6 + 1.2z = (-2.4 + 1.6z) Solving 5.6 + 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. 5.6 + 1.2z + -1.6z = -2.4 + 1.6z + -1.6z Combine like terms: 1.2z + -1.6z = -0.4z 5.6 + -0.4z = -2.4 + 1.6z + -1.6z Combine like terms: 1.6z + -1.6z = 0.0 5.6 + -0.4z = -2.4 + 0.0 5.6 + -0.4z = -2.4 Add '-5.6' to each side of the equation. 5.6 + -5.6 + -0.4z = -2.4 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + -0.4z = -2.4 + -5.6 -0.4z = -2.4 + -5.6 Combine like terms: -2.4 + -5.6 = -8 -0.4z = -8 Divide each side by '-0.4'. z = 20 Simplifying z = 20
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