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Simplifying 0.5(3z + 7) + 6.1 = 6.1(3z + -4) Reorder the terms: 0.5(7 + 3z) + 6.1 = 6.1(3z + -4) (7 * 0.5 + 3z * 0.5) + 6.1 = 6.1(3z + -4) (3.5 + 1.5z) + 6.1 = 6.1(3z + -4) Reorder the terms: 3.5 + 6.1 + 1.5z = 6.1(3z + -4) Combine like terms: 3.5 + 6.1 = 9.6 9.6 + 1.5z = 6.1(3z + -4) Reorder the terms: 9.6 + 1.5z = 6.1(-4 + 3z) 9.6 + 1.5z = (-4 * 6.1 + 3z * 6.1) 9.6 + 1.5z = (-24.4 + 18.3z) Solving 9.6 + 1.5z = -24.4 + 18.3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-18.3z' to each side of the equation. 9.6 + 1.5z + -18.3z = -24.4 + 18.3z + -18.3z Combine like terms: 1.5z + -18.3z = -16.8z 9.6 + -16.8z = -24.4 + 18.3z + -18.3z Combine like terms: 18.3z + -18.3z = 0.0 9.6 + -16.8z = -24.4 + 0.0 9.6 + -16.8z = -24.4 Add '-9.6' to each side of the equation. 9.6 + -9.6 + -16.8z = -24.4 + -9.6 Combine like terms: 9.6 + -9.6 = 0.0 0.0 + -16.8z = -24.4 + -9.6 -16.8z = -24.4 + -9.6 Combine like terms: -24.4 + -9.6 = -34 -16.8z = -34 Divide each side by '-16.8'. z = 2.023809524 Simplifying z = 2.023809524
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