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Simplifying 0.5(4z + 7) + 1.7 = 0.7(4z + -4) Reorder the terms: 0.5(7 + 4z) + 1.7 = 0.7(4z + -4) (7 * 0.5 + 4z * 0.5) + 1.7 = 0.7(4z + -4) (3.5 + 2z) + 1.7 = 0.7(4z + -4) Reorder the terms: 3.5 + 1.7 + 2z = 0.7(4z + -4) Combine like terms: 3.5 + 1.7 = 5.2 5.2 + 2z = 0.7(4z + -4) Reorder the terms: 5.2 + 2z = 0.7(-4 + 4z) 5.2 + 2z = (-4 * 0.7 + 4z * 0.7) 5.2 + 2z = (-2.8 + 2.8z) Solving 5.2 + 2z = -2.8 + 2.8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.8z' to each side of the equation. 5.2 + 2z + -2.8z = -2.8 + 2.8z + -2.8z Combine like terms: 2z + -2.8z = -0.8z 5.2 + -0.8z = -2.8 + 2.8z + -2.8z Combine like terms: 2.8z + -2.8z = 0.0 5.2 + -0.8z = -2.8 + 0.0 5.2 + -0.8z = -2.8 Add '-5.2' to each side of the equation. 5.2 + -5.2 + -0.8z = -2.8 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 0.0 + -0.8z = -2.8 + -5.2 -0.8z = -2.8 + -5.2 Combine like terms: -2.8 + -5.2 = -8 -0.8z = -8 Divide each side by '-0.8'. z = 10 Simplifying z = 10
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