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Simplifying 0.3(2z + 7) + 2.9 = 0.5(2z + -6) Reorder the terms: 0.3(7 + 2z) + 2.9 = 0.5(2z + -6) (7 * 0.3 + 2z * 0.3) + 2.9 = 0.5(2z + -6) (2.1 + 0.6z) + 2.9 = 0.5(2z + -6) Reorder the terms: 2.1 + 2.9 + 0.6z = 0.5(2z + -6) Combine like terms: 2.1 + 2.9 = 5 5 + 0.6z = 0.5(2z + -6) Reorder the terms: 5 + 0.6z = 0.5(-6 + 2z) 5 + 0.6z = (-6 * 0.5 + 2z * 0.5) 5 + 0.6z = (-3 + 1z) Solving 5 + 0.6z = -3 + 1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1z' to each side of the equation. 5 + 0.6z + -1z = -3 + 1z + -1z Combine like terms: 0.6z + -1z = -0.4z 5 + -0.4z = -3 + 1z + -1z Combine like terms: 1z + -1z = 0 5 + -0.4z = -3 + 0 5 + -0.4z = -3 Add '-5' to each side of the equation. 5 + -5 + -0.4z = -3 + -5 Combine like terms: 5 + -5 = 0 0 + -0.4z = -3 + -5 -0.4z = -3 + -5 Combine like terms: -3 + -5 = -8 -0.4z = -8 Divide each side by '-0.4'. z = 20 Simplifying z = 20
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