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Simplifying 0.5(3z + 5) + -17.3 = 0.7(3z + -6) Reorder the terms: 0.5(5 + 3z) + -17.3 = 0.7(3z + -6) (5 * 0.5 + 3z * 0.5) + -17.3 = 0.7(3z + -6) (2.5 + 1.5z) + -17.3 = 0.7(3z + -6) Reorder the terms: 2.5 + -17.3 + 1.5z = 0.7(3z + -6) Combine like terms: 2.5 + -17.3 = -14.8 -14.8 + 1.5z = 0.7(3z + -6) Reorder the terms: -14.8 + 1.5z = 0.7(-6 + 3z) -14.8 + 1.5z = (-6 * 0.7 + 3z * 0.7) -14.8 + 1.5z = (-4.2 + 2.1z) Solving -14.8 + 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. -14.8 + 1.5z + -2.1z = -4.2 + 2.1z + -2.1z Combine like terms: 1.5z + -2.1z = -0.6z -14.8 + -0.6z = -4.2 + 2.1z + -2.1z Combine like terms: 2.1z + -2.1z = 0.0 -14.8 + -0.6z = -4.2 + 0.0 -14.8 + -0.6z = -4.2 Add '14.8' to each side of the equation. -14.8 + 14.8 + -0.6z = -4.2 + 14.8 Combine like terms: -14.8 + 14.8 = 0.0 0.0 + -0.6z = -4.2 + 14.8 -0.6z = -4.2 + 14.8 Combine like terms: -4.2 + 14.8 = 10.6 -0.6z = 10.6 Divide each side by '-0.6'. z = -17.66666667 Simplifying z = -17.66666667
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