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Simplifying 0.4(4z + 7) + 9.6 = 0.6(4z + -6) Reorder the terms: 0.4(7 + 4z) + 9.6 = 0.6(4z + -6) (7 * 0.4 + 4z * 0.4) + 9.6 = 0.6(4z + -6) (2.8 + 1.6z) + 9.6 = 0.6(4z + -6) Reorder the terms: 2.8 + 9.6 + 1.6z = 0.6(4z + -6) Combine like terms: 2.8 + 9.6 = 12.4 12.4 + 1.6z = 0.6(4z + -6) Reorder the terms: 12.4 + 1.6z = 0.6(-6 + 4z) 12.4 + 1.6z = (-6 * 0.6 + 4z * 0.6) 12.4 + 1.6z = (-3.6 + 2.4z) Solving 12.4 + 1.6z = -3.6 + 2.4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.4z' to each side of the equation. 12.4 + 1.6z + -2.4z = -3.6 + 2.4z + -2.4z Combine like terms: 1.6z + -2.4z = -0.8z 12.4 + -0.8z = -3.6 + 2.4z + -2.4z Combine like terms: 2.4z + -2.4z = 0.0 12.4 + -0.8z = -3.6 + 0.0 12.4 + -0.8z = -3.6 Add '-12.4' to each side of the equation. 12.4 + -12.4 + -0.8z = -3.6 + -12.4 Combine like terms: 12.4 + -12.4 = 0.0 0.0 + -0.8z = -3.6 + -12.4 -0.8z = -3.6 + -12.4 Combine like terms: -3.6 + -12.4 = -16 -0.8z = -16 Divide each side by '-0.8'. z = 20 Simplifying z = 20
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