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Simplifying 0.5(3z + 6) + 12.2 = 0.7(3z + -4) Reorder the terms: 0.5(6 + 3z) + 12.2 = 0.7(3z + -4) (6 * 0.5 + 3z * 0.5) + 12.2 = 0.7(3z + -4) (3 + 1.5z) + 12.2 = 0.7(3z + -4) Reorder the terms: 3 + 12.2 + 1.5z = 0.7(3z + -4) Combine like terms: 3 + 12.2 = 15.2 15.2 + 1.5z = 0.7(3z + -4) Reorder the terms: 15.2 + 1.5z = 0.7(-4 + 3z) 15.2 + 1.5z = (-4 * 0.7 + 3z * 0.7) 15.2 + 1.5z = (-2.8 + 2.1z) Solving 15.2 + 1.5z = -2.8 + 2.1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.1z' to each side of the equation. 15.2 + 1.5z + -2.1z = -2.8 + 2.1z + -2.1z Combine like terms: 1.5z + -2.1z = -0.6z 15.2 + -0.6z = -2.8 + 2.1z + -2.1z Combine like terms: 2.1z + -2.1z = 0.0 15.2 + -0.6z = -2.8 + 0.0 15.2 + -0.6z = -2.8 Add '-15.2' to each side of the equation. 15.2 + -15.2 + -0.6z = -2.8 + -15.2 Combine like terms: 15.2 + -15.2 = 0.0 0.0 + -0.6z = -2.8 + -15.2 -0.6z = -2.8 + -15.2 Combine like terms: -2.8 + -15.2 = -18 -0.6z = -18 Divide each side by '-0.6'. z = 30 Simplifying z = 30
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