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Simplifying 0.5(3z + 6) + 17.5 = 0.7(3z + -5) Reorder the terms: 0.5(6 + 3z) + 17.5 = 0.7(3z + -5) (6 * 0.5 + 3z * 0.5) + 17.5 = 0.7(3z + -5) (3 + 1.5z) + 17.5 = 0.7(3z + -5) Reorder the terms: 3 + 17.5 + 1.5z = 0.7(3z + -5) Combine like terms: 3 + 17.5 = 20.5 20.5 + 1.5z = 0.7(3z + -5) Reorder the terms: 20.5 + 1.5z = 0.7(-5 + 3z) 20.5 + 1.5z = (-5 * 0.7 + 3z * 0.7) 20.5 + 1.5z = (-3.5 + 2.1z) Solving 20.5 + 1.5z = -3.5 + 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. 20.5 + 1.5z + -2.1z = -3.5 + 2.1z + -2.1z Combine like terms: 1.5z + -2.1z = -0.6z 20.5 + -0.6z = -3.5 + 2.1z + -2.1z Combine like terms: 2.1z + -2.1z = 0.0 20.5 + -0.6z = -3.5 + 0.0 20.5 + -0.6z = -3.5 Add '-20.5' to each side of the equation. 20.5 + -20.5 + -0.6z = -3.5 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + -0.6z = -3.5 + -20.5 -0.6z = -3.5 + -20.5 Combine like terms: -3.5 + -20.5 = -24 -0.6z = -24 Divide each side by '-0.6'. z = 40 Simplifying z = 40
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