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Simplifying 4(6z + -1) + -5(z + 7) = 14(z + 1) Reorder the terms: 4(-1 + 6z) + -5(z + 7) = 14(z + 1) (-1 * 4 + 6z * 4) + -5(z + 7) = 14(z + 1) (-4 + 24z) + -5(z + 7) = 14(z + 1) Reorder the terms: -4 + 24z + -5(7 + z) = 14(z + 1) -4 + 24z + (7 * -5 + z * -5) = 14(z + 1) -4 + 24z + (-35 + -5z) = 14(z + 1) Reorder the terms: -4 + -35 + 24z + -5z = 14(z + 1) Combine like terms: -4 + -35 = -39 -39 + 24z + -5z = 14(z + 1) Combine like terms: 24z + -5z = 19z -39 + 19z = 14(z + 1) Reorder the terms: -39 + 19z = 14(1 + z) -39 + 19z = (1 * 14 + z * 14) -39 + 19z = (14 + 14z) Solving -39 + 19z = 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. -39 + 19z + -14z = 14 + 14z + -14z Combine like terms: 19z + -14z = 5z -39 + 5z = 14 + 14z + -14z Combine like terms: 14z + -14z = 0 -39 + 5z = 14 + 0 -39 + 5z = 14 Add '39' to each side of the equation. -39 + 39 + 5z = 14 + 39 Combine like terms: -39 + 39 = 0 0 + 5z = 14 + 39 5z = 14 + 39 Combine like terms: 14 + 39 = 53 5z = 53 Divide each side by '5'. z = 10.6 Simplifying z = 10.6
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