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Simplifying 0.4(4z + 7) + 18.2 = 0.6(4z + -5) Reorder the terms: 0.4(7 + 4z) + 18.2 = 0.6(4z + -5) (7 * 0.4 + 4z * 0.4) + 18.2 = 0.6(4z + -5) (2.8 + 1.6z) + 18.2 = 0.6(4z + -5) Reorder the terms: 2.8 + 18.2 + 1.6z = 0.6(4z + -5) Combine like terms: 2.8 + 18.2 = 21 21 + 1.6z = 0.6(4z + -5) Reorder the terms: 21 + 1.6z = 0.6(-5 + 4z) 21 + 1.6z = (-5 * 0.6 + 4z * 0.6) 21 + 1.6z = (-3 + 2.4z) Solving 21 + 1.6z = -3 + 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. 21 + 1.6z + -2.4z = -3 + 2.4z + -2.4z Combine like terms: 1.6z + -2.4z = -0.8z 21 + -0.8z = -3 + 2.4z + -2.4z Combine like terms: 2.4z + -2.4z = 0.0 21 + -0.8z = -3 + 0.0 21 + -0.8z = -3 Add '-21' to each side of the equation. 21 + -21 + -0.8z = -3 + -21 Combine like terms: 21 + -21 = 0 0 + -0.8z = -3 + -21 -0.8z = -3 + -21 Combine like terms: -3 + -21 = -24 -0.8z = -24 Divide each side by '-0.8'. z = 30 Simplifying z = 30
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