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Simplifying 0.4(2z + 7) + 18.4 = 0.7(2z + -4) Reorder the terms: 0.4(7 + 2z) + 18.4 = 0.7(2z + -4) (7 * 0.4 + 2z * 0.4) + 18.4 = 0.7(2z + -4) (2.8 + 0.8z) + 18.4 = 0.7(2z + -4) Reorder the terms: 2.8 + 18.4 + 0.8z = 0.7(2z + -4) Combine like terms: 2.8 + 18.4 = 21.2 21.2 + 0.8z = 0.7(2z + -4) Reorder the terms: 21.2 + 0.8z = 0.7(-4 + 2z) 21.2 + 0.8z = (-4 * 0.7 + 2z * 0.7) 21.2 + 0.8z = (-2.8 + 1.4z) Solving 21.2 + 0.8z = -2.8 + 1.4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.4z' to each side of the equation. 21.2 + 0.8z + -1.4z = -2.8 + 1.4z + -1.4z Combine like terms: 0.8z + -1.4z = -0.6z 21.2 + -0.6z = -2.8 + 1.4z + -1.4z Combine like terms: 1.4z + -1.4z = 0.0 21.2 + -0.6z = -2.8 + 0.0 21.2 + -0.6z = -2.8 Add '-21.2' to each side of the equation. 21.2 + -21.2 + -0.6z = -2.8 + -21.2 Combine like terms: 21.2 + -21.2 = 0.0 0.0 + -0.6z = -2.8 + -21.2 -0.6z = -2.8 + -21.2 Combine like terms: -2.8 + -21.2 = -24 -0.6z = -24 Divide each side by '-0.6'. z = 40 Simplifying z = 40
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