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Simplifying 4(5z + -1) + -5(z + 3) = 2(z + 1) Reorder the terms: 4(-1 + 5z) + -5(z + 3) = 2(z + 1) (-1 * 4 + 5z * 4) + -5(z + 3) = 2(z + 1) (-4 + 20z) + -5(z + 3) = 2(z + 1) Reorder the terms: -4 + 20z + -5(3 + z) = 2(z + 1) -4 + 20z + (3 * -5 + z * -5) = 2(z + 1) -4 + 20z + (-15 + -5z) = 2(z + 1) Reorder the terms: -4 + -15 + 20z + -5z = 2(z + 1) Combine like terms: -4 + -15 = -19 -19 + 20z + -5z = 2(z + 1) Combine like terms: 20z + -5z = 15z -19 + 15z = 2(z + 1) Reorder the terms: -19 + 15z = 2(1 + z) -19 + 15z = (1 * 2 + z * 2) -19 + 15z = (2 + 2z) Solving -19 + 15z = 2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -19 + 15z + -2z = 2 + 2z + -2z Combine like terms: 15z + -2z = 13z -19 + 13z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -19 + 13z = 2 + 0 -19 + 13z = 2 Add '19' to each side of the equation. -19 + 19 + 13z = 2 + 19 Combine like terms: -19 + 19 = 0 0 + 13z = 2 + 19 13z = 2 + 19 Combine like terms: 2 + 19 = 21 13z = 21 Divide each side by '13'. z = 1.615384615 Simplifying z = 1.615384615
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