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Simplifying 4(5z + -1) + -4(2 + 9) = 7(z + 1) Reorder the terms: 4(-1 + 5z) + -4(2 + 9) = 7(z + 1) (-1 * 4 + 5z * 4) + -4(2 + 9) = 7(z + 1) (-4 + 20z) + -4(2 + 9) = 7(z + 1) Combine like terms: 2 + 9 = 11 -4 + 20z + -4(11) = 7(z + 1) Multiply -4 * 11 -4 + 20z + -44 = 7(z + 1) Reorder the terms: -4 + -44 + 20z = 7(z + 1) Combine like terms: -4 + -44 = -48 -48 + 20z = 7(z + 1) Reorder the terms: -48 + 20z = 7(1 + z) -48 + 20z = (1 * 7 + z * 7) -48 + 20z = (7 + 7z) Solving -48 + 20z = 7 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. -48 + 20z + -7z = 7 + 7z + -7z Combine like terms: 20z + -7z = 13z -48 + 13z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -48 + 13z = 7 + 0 -48 + 13z = 7 Add '48' to each side of the equation. -48 + 48 + 13z = 7 + 48 Combine like terms: -48 + 48 = 0 0 + 13z = 7 + 48 13z = 7 + 48 Combine like terms: 7 + 48 = 55 13z = 55 Divide each side by '13'. z = 4.230769231 Simplifying z = 4.230769231
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