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Simplifying 0.5(3z + 7) + 10.3 = 0.7(3z + -6) Reorder the terms: 0.5(7 + 3z) + 10.3 = 0.7(3z + -6) (7 * 0.5 + 3z * 0.5) + 10.3 = 0.7(3z + -6) (3.5 + 1.5z) + 10.3 = 0.7(3z + -6) Reorder the terms: 3.5 + 10.3 + 1.5z = 0.7(3z + -6) Combine like terms: 3.5 + 10.3 = 13.8 13.8 + 1.5z = 0.7(3z + -6) Reorder the terms: 13.8 + 1.5z = 0.7(-6 + 3z) 13.8 + 1.5z = (-6 * 0.7 + 3z * 0.7) 13.8 + 1.5z = (-4.2 + 2.1z) Solving 13.8 + 1.5z = -4.2 + 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. 13.8 + 1.5z + -2.1z = -4.2 + 2.1z + -2.1z Combine like terms: 1.5z + -2.1z = -0.6z 13.8 + -0.6z = -4.2 + 2.1z + -2.1z Combine like terms: 2.1z + -2.1z = 0.0 13.8 + -0.6z = -4.2 + 0.0 13.8 + -0.6z = -4.2 Add '-13.8' to each side of the equation. 13.8 + -13.8 + -0.6z = -4.2 + -13.8 Combine like terms: 13.8 + -13.8 = 0.0 0.0 + -0.6z = -4.2 + -13.8 -0.6z = -4.2 + -13.8 Combine like terms: -4.2 + -13.8 = -18 -0.6z = -18 Divide each side by '-0.6'. z = 30 Simplifying z = 30
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