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Simplifying 0.4(3z + 5) + 3.5 = 0.7(3z + -5) Reorder the terms: 0.4(5 + 3z) + 3.5 = 0.7(3z + -5) (5 * 0.4 + 3z * 0.4) + 3.5 = 0.7(3z + -5) (2 + 1.2z) + 3.5 = 0.7(3z + -5) Reorder the terms: 2 + 3.5 + 1.2z = 0.7(3z + -5) Combine like terms: 2 + 3.5 = 5.5 5.5 + 1.2z = 0.7(3z + -5) Reorder the terms: 5.5 + 1.2z = 0.7(-5 + 3z) 5.5 + 1.2z = (-5 * 0.7 + 3z * 0.7) 5.5 + 1.2z = (-3.5 + 2.1z) Solving 5.5 + 1.2z = -3.5 + 2.1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.1z' to each side of the equation. 5.5 + 1.2z + -2.1z = -3.5 + 2.1z + -2.1z Combine like terms: 1.2z + -2.1z = -0.9z 5.5 + -0.9z = -3.5 + 2.1z + -2.1z Combine like terms: 2.1z + -2.1z = 0.0 5.5 + -0.9z = -3.5 + 0.0 5.5 + -0.9z = -3.5 Add '-5.5' to each side of the equation. 5.5 + -5.5 + -0.9z = -3.5 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -0.9z = -3.5 + -5.5 -0.9z = -3.5 + -5.5 Combine like terms: -3.5 + -5.5 = -9 -0.9z = -9 Divide each side by '-0.9'. z = 10 Simplifying z = 10
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