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Simplifying 0.4(2z + 7) + 5.7 = 0.7(2z + -5) Reorder the terms: 0.4(7 + 2z) + 5.7 = 0.7(2z + -5) (7 * 0.4 + 2z * 0.4) + 5.7 = 0.7(2z + -5) (2.8 + 0.8z) + 5.7 = 0.7(2z + -5) Reorder the terms: 2.8 + 5.7 + 0.8z = 0.7(2z + -5) Combine like terms: 2.8 + 5.7 = 8.5 8.5 + 0.8z = 0.7(2z + -5) Reorder the terms: 8.5 + 0.8z = 0.7(-5 + 2z) 8.5 + 0.8z = (-5 * 0.7 + 2z * 0.7) 8.5 + 0.8z = (-3.5 + 1.4z) Solving 8.5 + 0.8z = -3.5 + 1.4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.4z' to each side of the equation. 8.5 + 0.8z + -1.4z = -3.5 + 1.4z + -1.4z Combine like terms: 0.8z + -1.4z = -0.6z 8.5 + -0.6z = -3.5 + 1.4z + -1.4z Combine like terms: 1.4z + -1.4z = 0.0 8.5 + -0.6z = -3.5 + 0.0 8.5 + -0.6z = -3.5 Add '-8.5' to each side of the equation. 8.5 + -8.5 + -0.6z = -3.5 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -0.6z = -3.5 + -8.5 -0.6z = -3.5 + -8.5 Combine like terms: -3.5 + -8.5 = -12 -0.6z = -12 Divide each side by '-0.6'. z = 20 Simplifying z = 20
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