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Simplifying 0.3(2z + 5) + 18.3 = 0.7(2z + -6) Reorder the terms: 0.3(5 + 2z) + 18.3 = 0.7(2z + -6) (5 * 0.3 + 2z * 0.3) + 18.3 = 0.7(2z + -6) (1.5 + 0.6z) + 18.3 = 0.7(2z + -6) Reorder the terms: 1.5 + 18.3 + 0.6z = 0.7(2z + -6) Combine like terms: 1.5 + 18.3 = 19.8 19.8 + 0.6z = 0.7(2z + -6) Reorder the terms: 19.8 + 0.6z = 0.7(-6 + 2z) 19.8 + 0.6z = (-6 * 0.7 + 2z * 0.7) 19.8 + 0.6z = (-4.2 + 1.4z) Solving 19.8 + 0.6z = -4.2 + 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. 19.8 + 0.6z + -1.4z = -4.2 + 1.4z + -1.4z Combine like terms: 0.6z + -1.4z = -0.8z 19.8 + -0.8z = -4.2 + 1.4z + -1.4z Combine like terms: 1.4z + -1.4z = 0.0 19.8 + -0.8z = -4.2 + 0.0 19.8 + -0.8z = -4.2 Add '-19.8' to each side of the equation. 19.8 + -19.8 + -0.8z = -4.2 + -19.8 Combine like terms: 19.8 + -19.8 = 0.0 0.0 + -0.8z = -4.2 + -19.8 -0.8z = -4.2 + -19.8 Combine like terms: -4.2 + -19.8 = -24 -0.8z = -24 Divide each side by '-0.8'. z = 30 Simplifying z = 30
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