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Simplifying 5(4z + -1) + -2(z + 7) = 13(z + -1) Reorder the terms: 5(-1 + 4z) + -2(z + 7) = 13(z + -1) (-1 * 5 + 4z * 5) + -2(z + 7) = 13(z + -1) (-5 + 20z) + -2(z + 7) = 13(z + -1) Reorder the terms: -5 + 20z + -2(7 + z) = 13(z + -1) -5 + 20z + (7 * -2 + z * -2) = 13(z + -1) -5 + 20z + (-14 + -2z) = 13(z + -1) Reorder the terms: -5 + -14 + 20z + -2z = 13(z + -1) Combine like terms: -5 + -14 = -19 -19 + 20z + -2z = 13(z + -1) Combine like terms: 20z + -2z = 18z -19 + 18z = 13(z + -1) Reorder the terms: -19 + 18z = 13(-1 + z) -19 + 18z = (-1 * 13 + z * 13) -19 + 18z = (-13 + 13z) Solving -19 + 18z = -13 + 13z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-13z' to each side of the equation. -19 + 18z + -13z = -13 + 13z + -13z Combine like terms: 18z + -13z = 5z -19 + 5z = -13 + 13z + -13z Combine like terms: 13z + -13z = 0 -19 + 5z = -13 + 0 -19 + 5z = -13 Add '19' to each side of the equation. -19 + 19 + 5z = -13 + 19 Combine like terms: -19 + 19 = 0 0 + 5z = -13 + 19 5z = -13 + 19 Combine like terms: -13 + 19 = 6 5z = 6 Divide each side by '5'. z = 1.2 Simplifying z = 1.2
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