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Simplifying 6(4z + -1) + -5(z + 3) = 12(z + 1) Reorder the terms: 6(-1 + 4z) + -5(z + 3) = 12(z + 1) (-1 * 6 + 4z * 6) + -5(z + 3) = 12(z + 1) (-6 + 24z) + -5(z + 3) = 12(z + 1) Reorder the terms: -6 + 24z + -5(3 + z) = 12(z + 1) -6 + 24z + (3 * -5 + z * -5) = 12(z + 1) -6 + 24z + (-15 + -5z) = 12(z + 1) Reorder the terms: -6 + -15 + 24z + -5z = 12(z + 1) Combine like terms: -6 + -15 = -21 -21 + 24z + -5z = 12(z + 1) Combine like terms: 24z + -5z = 19z -21 + 19z = 12(z + 1) Reorder the terms: -21 + 19z = 12(1 + z) -21 + 19z = (1 * 12 + z * 12) -21 + 19z = (12 + 12z) Solving -21 + 19z = 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. -21 + 19z + -12z = 12 + 12z + -12z Combine like terms: 19z + -12z = 7z -21 + 7z = 12 + 12z + -12z Combine like terms: 12z + -12z = 0 -21 + 7z = 12 + 0 -21 + 7z = 12 Add '21' to each side of the equation. -21 + 21 + 7z = 12 + 21 Combine like terms: -21 + 21 = 0 0 + 7z = 12 + 21 7z = 12 + 21 Combine like terms: 12 + 21 = 33 7z = 33 Divide each side by '7'. z = 4.714285714 Simplifying z = 4.714285714
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