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Simplifying 5 + -1(3 + -2z) + 4 = 5(2z + -3) + -1(3z + -2) 5 + (3 * -1 + -2z * -1) + 4 = 5(2z + -3) + -1(3z + -2) 5 + (-3 + 2z) + 4 = 5(2z + -3) + -1(3z + -2) Reorder the terms: 5 + -3 + 4 + 2z = 5(2z + -3) + -1(3z + -2) Combine like terms: 5 + -3 = 2 2 + 4 + 2z = 5(2z + -3) + -1(3z + -2) Combine like terms: 2 + 4 = 6 6 + 2z = 5(2z + -3) + -1(3z + -2) Reorder the terms: 6 + 2z = 5(-3 + 2z) + -1(3z + -2) 6 + 2z = (-3 * 5 + 2z * 5) + -1(3z + -2) 6 + 2z = (-15 + 10z) + -1(3z + -2) Reorder the terms: 6 + 2z = -15 + 10z + -1(-2 + 3z) 6 + 2z = -15 + 10z + (-2 * -1 + 3z * -1) 6 + 2z = -15 + 10z + (2 + -3z) Reorder the terms: 6 + 2z = -15 + 2 + 10z + -3z Combine like terms: -15 + 2 = -13 6 + 2z = -13 + 10z + -3z Combine like terms: 10z + -3z = 7z 6 + 2z = -13 + 7z Solving 6 + 2z = -13 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. 6 + 2z + -7z = -13 + 7z + -7z Combine like terms: 2z + -7z = -5z 6 + -5z = -13 + 7z + -7z Combine like terms: 7z + -7z = 0 6 + -5z = -13 + 0 6 + -5z = -13 Add '-6' to each side of the equation. 6 + -6 + -5z = -13 + -6 Combine like terms: 6 + -6 = 0 0 + -5z = -13 + -6 -5z = -13 + -6 Combine like terms: -13 + -6 = -19 -5z = -19 Divide each side by '-5'. z = 3.8 Simplifying z = 3.8
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