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Simplifying 5(4z + -1) + -2(z + 4) = 12(z + 1) Reorder the terms: 5(-1 + 4z) + -2(z + 4) = 12(z + 1) (-1 * 5 + 4z * 5) + -2(z + 4) = 12(z + 1) (-5 + 20z) + -2(z + 4) = 12(z + 1) Reorder the terms: -5 + 20z + -2(4 + z) = 12(z + 1) -5 + 20z + (4 * -2 + z * -2) = 12(z + 1) -5 + 20z + (-8 + -2z) = 12(z + 1) Reorder the terms: -5 + -8 + 20z + -2z = 12(z + 1) Combine like terms: -5 + -8 = -13 -13 + 20z + -2z = 12(z + 1) Combine like terms: 20z + -2z = 18z -13 + 18z = 12(z + 1) Reorder the terms: -13 + 18z = 12(1 + z) -13 + 18z = (1 * 12 + z * 12) -13 + 18z = (12 + 12z) Solving -13 + 18z = 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. -13 + 18z + -12z = 12 + 12z + -12z Combine like terms: 18z + -12z = 6z -13 + 6z = 12 + 12z + -12z Combine like terms: 12z + -12z = 0 -13 + 6z = 12 + 0 -13 + 6z = 12 Add '13' to each side of the equation. -13 + 13 + 6z = 12 + 13 Combine like terms: -13 + 13 = 0 0 + 6z = 12 + 13 6z = 12 + 13 Combine like terms: 12 + 13 = 25 6z = 25 Divide each side by '6'. z = 4.166666667 Simplifying z = 4.166666667
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