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Simplifying 4[z + -1(5z + 41) + 5] = 5(z + 9) Reorder the terms: 4[z + -1(41 + 5z) + 5] = 5(z + 9) 4[z + (41 * -1 + 5z * -1) + 5] = 5(z + 9) 4[z + (-41 + -5z) + 5] = 5(z + 9) Reorder the terms: 4[-41 + 5 + z + -5z] = 5(z + 9) Combine like terms: -41 + 5 = -36 4[-36 + z + -5z] = 5(z + 9) Combine like terms: z + -5z = -4z 4[-36 + -4z] = 5(z + 9) [-36 * 4 + -4z * 4] = 5(z + 9) [-144 + -16z] = 5(z + 9) Reorder the terms: -144 + -16z = 5(9 + z) -144 + -16z = (9 * 5 + z * 5) -144 + -16z = (45 + 5z) Solving -144 + -16z = 45 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -144 + -16z + -5z = 45 + 5z + -5z Combine like terms: -16z + -5z = -21z -144 + -21z = 45 + 5z + -5z Combine like terms: 5z + -5z = 0 -144 + -21z = 45 + 0 -144 + -21z = 45 Add '144' to each side of the equation. -144 + 144 + -21z = 45 + 144 Combine like terms: -144 + 144 = 0 0 + -21z = 45 + 144 -21z = 45 + 144 Combine like terms: 45 + 144 = 189 -21z = 189 Divide each side by '-21'. z = -9 Simplifying z = -9
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