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Simplifying 5(6z + -1) + -4(z + 5) = 22(z + 1) Reorder the terms: 5(-1 + 6z) + -4(z + 5) = 22(z + 1) (-1 * 5 + 6z * 5) + -4(z + 5) = 22(z + 1) (-5 + 30z) + -4(z + 5) = 22(z + 1) Reorder the terms: -5 + 30z + -4(5 + z) = 22(z + 1) -5 + 30z + (5 * -4 + z * -4) = 22(z + 1) -5 + 30z + (-20 + -4z) = 22(z + 1) Reorder the terms: -5 + -20 + 30z + -4z = 22(z + 1) Combine like terms: -5 + -20 = -25 -25 + 30z + -4z = 22(z + 1) Combine like terms: 30z + -4z = 26z -25 + 26z = 22(z + 1) Reorder the terms: -25 + 26z = 22(1 + z) -25 + 26z = (1 * 22 + z * 22) -25 + 26z = (22 + 22z) Solving -25 + 26z = 22 + 22z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-22z' to each side of the equation. -25 + 26z + -22z = 22 + 22z + -22z Combine like terms: 26z + -22z = 4z -25 + 4z = 22 + 22z + -22z Combine like terms: 22z + -22z = 0 -25 + 4z = 22 + 0 -25 + 4z = 22 Add '25' to each side of the equation. -25 + 25 + 4z = 22 + 25 Combine like terms: -25 + 25 = 0 0 + 4z = 22 + 25 4z = 22 + 25 Combine like terms: 22 + 25 = 47 4z = 47 Divide each side by '4'. z = 11.75 Simplifying z = 11.75
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