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Simplifying 0.4(3z + 6) + 18.6 = 0.6(3z + -5) Reorder the terms: 0.4(6 + 3z) + 18.6 = 0.6(3z + -5) (6 * 0.4 + 3z * 0.4) + 18.6 = 0.6(3z + -5) (2.4 + 1.2z) + 18.6 = 0.6(3z + -5) Reorder the terms: 2.4 + 18.6 + 1.2z = 0.6(3z + -5) Combine like terms: 2.4 + 18.6 = 21 21 + 1.2z = 0.6(3z + -5) Reorder the terms: 21 + 1.2z = 0.6(-5 + 3z) 21 + 1.2z = (-5 * 0.6 + 3z * 0.6) 21 + 1.2z = (-3 + 1.8z) Solving 21 + 1.2z = -3 + 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. 21 + 1.2z + -1.8z = -3 + 1.8z + -1.8z Combine like terms: 1.2z + -1.8z = -0.6z 21 + -0.6z = -3 + 1.8z + -1.8z Combine like terms: 1.8z + -1.8z = 0.0 21 + -0.6z = -3 + 0.0 21 + -0.6z = -3 Add '-21' to each side of the equation. 21 + -21 + -0.6z = -3 + -21 Combine like terms: 21 + -21 = 0 0 + -0.6z = -3 + -21 -0.6z = -3 + -21 Combine like terms: -3 + -21 = -24 -0.6z = -24 Divide each side by '-0.6'. z = 40 Simplifying z = 40
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