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Simplifying 5(4z + -1) + -2(z + 6) = 12z + 1 Reorder the terms: 5(-1 + 4z) + -2(z + 6) = 12z + 1 (-1 * 5 + 4z * 5) + -2(z + 6) = 12z + 1 (-5 + 20z) + -2(z + 6) = 12z + 1 Reorder the terms: -5 + 20z + -2(6 + z) = 12z + 1 -5 + 20z + (6 * -2 + z * -2) = 12z + 1 -5 + 20z + (-12 + -2z) = 12z + 1 Reorder the terms: -5 + -12 + 20z + -2z = 12z + 1 Combine like terms: -5 + -12 = -17 -17 + 20z + -2z = 12z + 1 Combine like terms: 20z + -2z = 18z -17 + 18z = 12z + 1 Reorder the terms: -17 + 18z = 1 + 12z Solving -17 + 18z = 1 + 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. -17 + 18z + -12z = 1 + 12z + -12z Combine like terms: 18z + -12z = 6z -17 + 6z = 1 + 12z + -12z Combine like terms: 12z + -12z = 0 -17 + 6z = 1 + 0 -17 + 6z = 1 Add '17' to each side of the equation. -17 + 17 + 6z = 1 + 17 Combine like terms: -17 + 17 = 0 0 + 6z = 1 + 17 6z = 1 + 17 Combine like terms: 1 + 17 = 18 6z = 18 Divide each side by '6'. z = 3 Simplifying z = 3
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