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Simplifying 0.4(3z + 7) + 12.8 = 0.6(3z + -4) Reorder the terms: 0.4(7 + 3z) + 12.8 = 0.6(3z + -4) (7 * 0.4 + 3z * 0.4) + 12.8 = 0.6(3z + -4) (2.8 + 1.2z) + 12.8 = 0.6(3z + -4) Reorder the terms: 2.8 + 12.8 + 1.2z = 0.6(3z + -4) Combine like terms: 2.8 + 12.8 = 15.6 15.6 + 1.2z = 0.6(3z + -4) Reorder the terms: 15.6 + 1.2z = 0.6(-4 + 3z) 15.6 + 1.2z = (-4 * 0.6 + 3z * 0.6) 15.6 + 1.2z = (-2.4 + 1.8z) Solving 15.6 + 1.2z = -2.4 + 1.8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.8z' to each side of the equation. 15.6 + 1.2z + -1.8z = -2.4 + 1.8z + -1.8z Combine like terms: 1.2z + -1.8z = -0.6z 15.6 + -0.6z = -2.4 + 1.8z + -1.8z Combine like terms: 1.8z + -1.8z = 0.0 15.6 + -0.6z = -2.4 + 0.0 15.6 + -0.6z = -2.4 Add '-15.6' to each side of the equation. 15.6 + -15.6 + -0.6z = -2.4 + -15.6 Combine like terms: 15.6 + -15.6 = 0.0 0.0 + -0.6z = -2.4 + -15.6 -0.6z = -2.4 + -15.6 Combine like terms: -2.4 + -15.6 = -18 -0.6z = -18 Divide each side by '-0.6'. z = 30 Simplifying z = 30
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