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Simplifying 0.3(2z + 6) + 11.7 = 0.5(2z + -5) Reorder the terms: 0.3(6 + 2z) + 11.7 = 0.5(2z + -5) (6 * 0.3 + 2z * 0.3) + 11.7 = 0.5(2z + -5) (1.8 + 0.6z) + 11.7 = 0.5(2z + -5) Reorder the terms: 1.8 + 11.7 + 0.6z = 0.5(2z + -5) Combine like terms: 1.8 + 11.7 = 13.5 13.5 + 0.6z = 0.5(2z + -5) Reorder the terms: 13.5 + 0.6z = 0.5(-5 + 2z) 13.5 + 0.6z = (-5 * 0.5 + 2z * 0.5) 13.5 + 0.6z = (-2.5 + 1z) Solving 13.5 + 0.6z = -2.5 + 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. 13.5 + 0.6z + -1z = -2.5 + 1z + -1z Combine like terms: 0.6z + -1z = -0.4z 13.5 + -0.4z = -2.5 + 1z + -1z Combine like terms: 1z + -1z = 0 13.5 + -0.4z = -2.5 + 0 13.5 + -0.4z = -2.5 Add '-13.5' to each side of the equation. 13.5 + -13.5 + -0.4z = -2.5 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -0.4z = -2.5 + -13.5 -0.4z = -2.5 + -13.5 Combine like terms: -2.5 + -13.5 = -16 -0.4z = -16 Divide each side by '-0.4'. z = 40 Simplifying z = 40
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