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Simplifying 6(4z + -1) + -4(z + 3) = 7(z + 1) Reorder the terms: 6(-1 + 4z) + -4(z + 3) = 7(z + 1) (-1 * 6 + 4z * 6) + -4(z + 3) = 7(z + 1) (-6 + 24z) + -4(z + 3) = 7(z + 1) Reorder the terms: -6 + 24z + -4(3 + z) = 7(z + 1) -6 + 24z + (3 * -4 + z * -4) = 7(z + 1) -6 + 24z + (-12 + -4z) = 7(z + 1) Reorder the terms: -6 + -12 + 24z + -4z = 7(z + 1) Combine like terms: -6 + -12 = -18 -18 + 24z + -4z = 7(z + 1) Combine like terms: 24z + -4z = 20z -18 + 20z = 7(z + 1) Reorder the terms: -18 + 20z = 7(1 + z) -18 + 20z = (1 * 7 + z * 7) -18 + 20z = (7 + 7z) Solving -18 + 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. -18 + 20z + -7z = 7 + 7z + -7z Combine like terms: 20z + -7z = 13z -18 + 13z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -18 + 13z = 7 + 0 -18 + 13z = 7 Add '18' to each side of the equation. -18 + 18 + 13z = 7 + 18 Combine like terms: -18 + 18 = 0 0 + 13z = 7 + 18 13z = 7 + 18 Combine like terms: 7 + 18 = 25 13z = 25 Divide each side by '13'. z = 1.923076923 Simplifying z = 1.923076923
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