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Simplifying 4(6z + -1) + -3(z + 3) = 14(z + 1) Reorder the terms: 4(-1 + 6z) + -3(z + 3) = 14(z + 1) (-1 * 4 + 6z * 4) + -3(z + 3) = 14(z + 1) (-4 + 24z) + -3(z + 3) = 14(z + 1) Reorder the terms: -4 + 24z + -3(3 + z) = 14(z + 1) -4 + 24z + (3 * -3 + z * -3) = 14(z + 1) -4 + 24z + (-9 + -3z) = 14(z + 1) Reorder the terms: -4 + -9 + 24z + -3z = 14(z + 1) Combine like terms: -4 + -9 = -13 -13 + 24z + -3z = 14(z + 1) Combine like terms: 24z + -3z = 21z -13 + 21z = 14(z + 1) Reorder the terms: -13 + 21z = 14(1 + z) -13 + 21z = (1 * 14 + z * 14) -13 + 21z = (14 + 14z) Solving -13 + 21z = 14 + 14z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-14z' to each side of the equation. -13 + 21z + -14z = 14 + 14z + -14z Combine like terms: 21z + -14z = 7z -13 + 7z = 14 + 14z + -14z Combine like terms: 14z + -14z = 0 -13 + 7z = 14 + 0 -13 + 7z = 14 Add '13' to each side of the equation. -13 + 13 + 7z = 14 + 13 Combine like terms: -13 + 13 = 0 0 + 7z = 14 + 13 7z = 14 + 13 Combine like terms: 14 + 13 = 27 7z = 27 Divide each side by '7'. z = 3.857142857 Simplifying z = 3.857142857
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