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Simplifying 0.5(3z + 7) + 3.1 = 0.6(3z + -4) Reorder the terms: 0.5(7 + 3z) + 3.1 = 0.6(3z + -4) (7 * 0.5 + 3z * 0.5) + 3.1 = 0.6(3z + -4) (3.5 + 1.5z) + 3.1 = 0.6(3z + -4) Reorder the terms: 3.5 + 3.1 + 1.5z = 0.6(3z + -4) Combine like terms: 3.5 + 3.1 = 6.6 6.6 + 1.5z = 0.6(3z + -4) Reorder the terms: 6.6 + 1.5z = 0.6(-4 + 3z) 6.6 + 1.5z = (-4 * 0.6 + 3z * 0.6) 6.6 + 1.5z = (-2.4 + 1.8z) Solving 6.6 + 1.5z = -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. 6.6 + 1.5z + -1.8z = -2.4 + 1.8z + -1.8z Combine like terms: 1.5z + -1.8z = -0.3z 6.6 + -0.3z = -2.4 + 1.8z + -1.8z Combine like terms: 1.8z + -1.8z = 0.0 6.6 + -0.3z = -2.4 + 0.0 6.6 + -0.3z = -2.4 Add '-6.6' to each side of the equation. 6.6 + -6.6 + -0.3z = -2.4 + -6.6 Combine like terms: 6.6 + -6.6 = 0.0 0.0 + -0.3z = -2.4 + -6.6 -0.3z = -2.4 + -6.6 Combine like terms: -2.4 + -6.6 = -9 -0.3z = -9 Divide each side by '-0.3'. z = 30 Simplifying z = 30
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