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Simplifying -20(z + 1) + 6(4z + -3) = 3(z + -5) + 8 Reorder the terms: -20(1 + z) + 6(4z + -3) = 3(z + -5) + 8 (1 * -20 + z * -20) + 6(4z + -3) = 3(z + -5) + 8 (-20 + -20z) + 6(4z + -3) = 3(z + -5) + 8 Reorder the terms: -20 + -20z + 6(-3 + 4z) = 3(z + -5) + 8 -20 + -20z + (-3 * 6 + 4z * 6) = 3(z + -5) + 8 -20 + -20z + (-18 + 24z) = 3(z + -5) + 8 Reorder the terms: -20 + -18 + -20z + 24z = 3(z + -5) + 8 Combine like terms: -20 + -18 = -38 -38 + -20z + 24z = 3(z + -5) + 8 Combine like terms: -20z + 24z = 4z -38 + 4z = 3(z + -5) + 8 Reorder the terms: -38 + 4z = 3(-5 + z) + 8 -38 + 4z = (-5 * 3 + z * 3) + 8 -38 + 4z = (-15 + 3z) + 8 Reorder the terms: -38 + 4z = -15 + 8 + 3z Combine like terms: -15 + 8 = -7 -38 + 4z = -7 + 3z Solving -38 + 4z = -7 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -38 + 4z + -3z = -7 + 3z + -3z Combine like terms: 4z + -3z = 1z -38 + 1z = -7 + 3z + -3z Combine like terms: 3z + -3z = 0 -38 + 1z = -7 + 0 -38 + 1z = -7 Add '38' to each side of the equation. -38 + 38 + 1z = -7 + 38 Combine like terms: -38 + 38 = 0 0 + 1z = -7 + 38 1z = -7 + 38 Combine like terms: -7 + 38 = 31 1z = 31 Divide each side by '1'. z = 31 Simplifying z = 31
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