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Simplifying 0.5(3z + 5) * 7.1 = 0.6(3z + -4) Reorder the terms: 0.5(5 + 3z) * 7.1 = 0.6(3z + -4) Reorder the terms for easier multiplication: 0.5 * 7.1(5 + 3z) = 0.6(3z + -4) Multiply 0.5 * 7.1 3.55(5 + 3z) = 0.6(3z + -4) (5 * 3.55 + 3z * 3.55) = 0.6(3z + -4) (17.75 + 10.65z) = 0.6(3z + -4) Reorder the terms: 17.75 + 10.65z = 0.6(-4 + 3z) 17.75 + 10.65z = (-4 * 0.6 + 3z * 0.6) 17.75 + 10.65z = (-2.4 + 1.8z) Solving 17.75 + 10.65z = -2.4 + 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. 17.75 + 10.65z + -1.8z = -2.4 + 1.8z + -1.8z Combine like terms: 10.65z + -1.8z = 8.85z 17.75 + 8.85z = -2.4 + 1.8z + -1.8z Combine like terms: 1.8z + -1.8z = 0.0 17.75 + 8.85z = -2.4 + 0.0 17.75 + 8.85z = -2.4 Add '-17.75' to each side of the equation. 17.75 + -17.75 + 8.85z = -2.4 + -17.75 Combine like terms: 17.75 + -17.75 = 0.00 0.00 + 8.85z = -2.4 + -17.75 8.85z = -2.4 + -17.75 Combine like terms: -2.4 + -17.75 = -20.15 8.85z = -20.15 Divide each side by '8.85'. z = -2.276836158 Simplifying z = -2.276836158
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