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Simplifying 4(6z + -1) + -4(z + 2) = 7(z + 1) Reorder the terms: 4(-1 + 6z) + -4(z + 2) = 7(z + 1) (-1 * 4 + 6z * 4) + -4(z + 2) = 7(z + 1) (-4 + 24z) + -4(z + 2) = 7(z + 1) Reorder the terms: -4 + 24z + -4(2 + z) = 7(z + 1) -4 + 24z + (2 * -4 + z * -4) = 7(z + 1) -4 + 24z + (-8 + -4z) = 7(z + 1) Reorder the terms: -4 + -8 + 24z + -4z = 7(z + 1) Combine like terms: -4 + -8 = -12 -12 + 24z + -4z = 7(z + 1) Combine like terms: 24z + -4z = 20z -12 + 20z = 7(z + 1) Reorder the terms: -12 + 20z = 7(1 + z) -12 + 20z = (1 * 7 + z * 7) -12 + 20z = (7 + 7z) Solving -12 + 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. -12 + 20z + -7z = 7 + 7z + -7z Combine like terms: 20z + -7z = 13z -12 + 13z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -12 + 13z = 7 + 0 -12 + 13z = 7 Add '12' to each side of the equation. -12 + 12 + 13z = 7 + 12 Combine like terms: -12 + 12 = 0 0 + 13z = 7 + 12 13z = 7 + 12 Combine like terms: 7 + 12 = 19 13z = 19 Divide each side by '13'. z = 1.461538462 Simplifying z = 1.461538462
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