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Simplifying 4(6z + -1) + -3(z + 8) = 6(z + 1) Reorder the terms: 4(-1 + 6z) + -3(z + 8) = 6(z + 1) (-1 * 4 + 6z * 4) + -3(z + 8) = 6(z + 1) (-4 + 24z) + -3(z + 8) = 6(z + 1) Reorder the terms: -4 + 24z + -3(8 + z) = 6(z + 1) -4 + 24z + (8 * -3 + z * -3) = 6(z + 1) -4 + 24z + (-24 + -3z) = 6(z + 1) Reorder the terms: -4 + -24 + 24z + -3z = 6(z + 1) Combine like terms: -4 + -24 = -28 -28 + 24z + -3z = 6(z + 1) Combine like terms: 24z + -3z = 21z -28 + 21z = 6(z + 1) Reorder the terms: -28 + 21z = 6(1 + z) -28 + 21z = (1 * 6 + z * 6) -28 + 21z = (6 + 6z) Solving -28 + 21z = 6 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -28 + 21z + -6z = 6 + 6z + -6z Combine like terms: 21z + -6z = 15z -28 + 15z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -28 + 15z = 6 + 0 -28 + 15z = 6 Add '28' to each side of the equation. -28 + 28 + 15z = 6 + 28 Combine like terms: -28 + 28 = 0 0 + 15z = 6 + 28 15z = 6 + 28 Combine like terms: 6 + 28 = 34 15z = 34 Divide each side by '15'. z = 2.266666667 Simplifying z = 2.266666667
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