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Simplifying 4(6z + -1) + -4(z + 4) = 7(z + 1) Reorder the terms: 4(-1 + 6z) + -4(z + 4) = 7(z + 1) (-1 * 4 + 6z * 4) + -4(z + 4) = 7(z + 1) (-4 + 24z) + -4(z + 4) = 7(z + 1) Reorder the terms: -4 + 24z + -4(4 + z) = 7(z + 1) -4 + 24z + (4 * -4 + z * -4) = 7(z + 1) -4 + 24z + (-16 + -4z) = 7(z + 1) Reorder the terms: -4 + -16 + 24z + -4z = 7(z + 1) Combine like terms: -4 + -16 = -20 -20 + 24z + -4z = 7(z + 1) Combine like terms: 24z + -4z = 20z -20 + 20z = 7(z + 1) Reorder the terms: -20 + 20z = 7(1 + z) -20 + 20z = (1 * 7 + z * 7) -20 + 20z = (7 + 7z) Solving -20 + 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. -20 + 20z + -7z = 7 + 7z + -7z Combine like terms: 20z + -7z = 13z -20 + 13z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -20 + 13z = 7 + 0 -20 + 13z = 7 Add '20' to each side of the equation. -20 + 20 + 13z = 7 + 20 Combine like terms: -20 + 20 = 0 0 + 13z = 7 + 20 13z = 7 + 20 Combine like terms: 7 + 20 = 27 13z = 27 Divide each side by '13'. z = 2.076923077 Simplifying z = 2.076923077
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