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Simplifying 6(4z + -1) + -5(z + 2) = 7(z + 1) Reorder the terms: 6(-1 + 4z) + -5(z + 2) = 7(z + 1) (-1 * 6 + 4z * 6) + -5(z + 2) = 7(z + 1) (-6 + 24z) + -5(z + 2) = 7(z + 1) Reorder the terms: -6 + 24z + -5(2 + z) = 7(z + 1) -6 + 24z + (2 * -5 + z * -5) = 7(z + 1) -6 + 24z + (-10 + -5z) = 7(z + 1) Reorder the terms: -6 + -10 + 24z + -5z = 7(z + 1) Combine like terms: -6 + -10 = -16 -16 + 24z + -5z = 7(z + 1) Combine like terms: 24z + -5z = 19z -16 + 19z = 7(z + 1) Reorder the terms: -16 + 19z = 7(1 + z) -16 + 19z = (1 * 7 + z * 7) -16 + 19z = (7 + 7z) Solving -16 + 19z = 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. -16 + 19z + -7z = 7 + 7z + -7z Combine like terms: 19z + -7z = 12z -16 + 12z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -16 + 12z = 7 + 0 -16 + 12z = 7 Add '16' to each side of the equation. -16 + 16 + 12z = 7 + 16 Combine like terms: -16 + 16 = 0 0 + 12z = 7 + 16 12z = 7 + 16 Combine like terms: 7 + 16 = 23 12z = 23 Divide each side by '12'. z = 1.916666667 Simplifying z = 1.916666667
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