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Simplifying 4(6z + -1) + -3(z + 2) = 12(z + 1) Reorder the terms: 4(-1 + 6z) + -3(z + 2) = 12(z + 1) (-1 * 4 + 6z * 4) + -3(z + 2) = 12(z + 1) (-4 + 24z) + -3(z + 2) = 12(z + 1) Reorder the terms: -4 + 24z + -3(2 + z) = 12(z + 1) -4 + 24z + (2 * -3 + z * -3) = 12(z + 1) -4 + 24z + (-6 + -3z) = 12(z + 1) Reorder the terms: -4 + -6 + 24z + -3z = 12(z + 1) Combine like terms: -4 + -6 = -10 -10 + 24z + -3z = 12(z + 1) Combine like terms: 24z + -3z = 21z -10 + 21z = 12(z + 1) Reorder the terms: -10 + 21z = 12(1 + z) -10 + 21z = (1 * 12 + z * 12) -10 + 21z = (12 + 12z) Solving -10 + 21z = 12 + 12z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-12z' to each side of the equation. -10 + 21z + -12z = 12 + 12z + -12z Combine like terms: 21z + -12z = 9z -10 + 9z = 12 + 12z + -12z Combine like terms: 12z + -12z = 0 -10 + 9z = 12 + 0 -10 + 9z = 12 Add '10' to each side of the equation. -10 + 10 + 9z = 12 + 10 Combine like terms: -10 + 10 = 0 0 + 9z = 12 + 10 9z = 12 + 10 Combine like terms: 12 + 10 = 22 9z = 22 Divide each side by '9'. z = 2.444444444 Simplifying z = 2.444444444
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