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Simplifying 4(7 + -1z) + -38 = 27z + -5(2 + 6z) (7 * 4 + -1z * 4) + -38 = 27z + -5(2 + 6z) (28 + -4z) + -38 = 27z + -5(2 + 6z) Reorder the terms: 28 + -38 + -4z = 27z + -5(2 + 6z) Combine like terms: 28 + -38 = -10 -10 + -4z = 27z + -5(2 + 6z) -10 + -4z = 27z + (2 * -5 + 6z * -5) -10 + -4z = 27z + (-10 + -30z) Reorder the terms: -10 + -4z = -10 + 27z + -30z Combine like terms: 27z + -30z = -3z -10 + -4z = -10 + -3z Add '10' to each side of the equation. -10 + 10 + -4z = -10 + 10 + -3z Combine like terms: -10 + 10 = 0 0 + -4z = -10 + 10 + -3z -4z = -10 + 10 + -3z Combine like terms: -10 + 10 = 0 -4z = 0 + -3z -4z = -3z Solving -4z = -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. -4z + 3z = -3z + 3z Combine like terms: -4z + 3z = -1z -1z = -3z + 3z Combine like terms: -3z + 3z = 0 -1z = 0 Divide each side by '-1'. z = 0 Simplifying z = 0
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