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Simplifying 0.3(3z + 7) + 22.5 = 0.6(3z + -4) Reorder the terms: 0.3(7 + 3z) + 22.5 = 0.6(3z + -4) (7 * 0.3 + 3z * 0.3) + 22.5 = 0.6(3z + -4) (2.1 + 0.9z) + 22.5 = 0.6(3z + -4) Reorder the terms: 2.1 + 22.5 + 0.9z = 0.6(3z + -4) Combine like terms: 2.1 + 22.5 = 24.6 24.6 + 0.9z = 0.6(3z + -4) Reorder the terms: 24.6 + 0.9z = 0.6(-4 + 3z) 24.6 + 0.9z = (-4 * 0.6 + 3z * 0.6) 24.6 + 0.9z = (-2.4 + 1.8z) Solving 24.6 + 0.9z = -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. 24.6 + 0.9z + -1.8z = -2.4 + 1.8z + -1.8z Combine like terms: 0.9z + -1.8z = -0.9z 24.6 + -0.9z = -2.4 + 1.8z + -1.8z Combine like terms: 1.8z + -1.8z = 0.0 24.6 + -0.9z = -2.4 + 0.0 24.6 + -0.9z = -2.4 Add '-24.6' to each side of the equation. 24.6 + -24.6 + -0.9z = -2.4 + -24.6 Combine like terms: 24.6 + -24.6 = 0.0 0.0 + -0.9z = -2.4 + -24.6 -0.9z = -2.4 + -24.6 Combine like terms: -2.4 + -24.6 = -27 -0.9z = -27 Divide each side by '-0.9'. z = 30 Simplifying z = 30
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