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Simplifying 6(4z + -1) + -4(z + 9) = 7(z + 1) Reorder the terms: 6(-1 + 4z) + -4(z + 9) = 7(z + 1) (-1 * 6 + 4z * 6) + -4(z + 9) = 7(z + 1) (-6 + 24z) + -4(z + 9) = 7(z + 1) Reorder the terms: -6 + 24z + -4(9 + z) = 7(z + 1) -6 + 24z + (9 * -4 + z * -4) = 7(z + 1) -6 + 24z + (-36 + -4z) = 7(z + 1) Reorder the terms: -6 + -36 + 24z + -4z = 7(z + 1) Combine like terms: -6 + -36 = -42 -42 + 24z + -4z = 7(z + 1) Combine like terms: 24z + -4z = 20z -42 + 20z = 7(z + 1) Reorder the terms: -42 + 20z = 7(1 + z) -42 + 20z = (1 * 7 + z * 7) -42 + 20z = (7 + 7z) Solving -42 + 20z = 7 + 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. -42 + 20z + -7z = 7 + 7z + -7z Combine like terms: 20z + -7z = 13z -42 + 13z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -42 + 13z = 7 + 0 -42 + 13z = 7 Add '42' to each side of the equation. -42 + 42 + 13z = 7 + 42 Combine like terms: -42 + 42 = 0 0 + 13z = 7 + 42 13z = 7 + 42 Combine like terms: 7 + 42 = 49 13z = 49 Divide each side by '13'. z = 3.769230769 Simplifying z = 3.769230769
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