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Simplifying 10(Z + -9) + -9(5 + -6Z) = 2(4Z + -1) + 5(1 + 2Z) Reorder the terms: 10(-9 + Z) + -9(5 + -6Z) = 2(4Z + -1) + 5(1 + 2Z) (-9 * 10 + Z * 10) + -9(5 + -6Z) = 2(4Z + -1) + 5(1 + 2Z) (-90 + 10Z) + -9(5 + -6Z) = 2(4Z + -1) + 5(1 + 2Z) -90 + 10Z + (5 * -9 + -6Z * -9) = 2(4Z + -1) + 5(1 + 2Z) -90 + 10Z + (-45 + 54Z) = 2(4Z + -1) + 5(1 + 2Z) Reorder the terms: -90 + -45 + 10Z + 54Z = 2(4Z + -1) + 5(1 + 2Z) Combine like terms: -90 + -45 = -135 -135 + 10Z + 54Z = 2(4Z + -1) + 5(1 + 2Z) Combine like terms: 10Z + 54Z = 64Z -135 + 64Z = 2(4Z + -1) + 5(1 + 2Z) Reorder the terms: -135 + 64Z = 2(-1 + 4Z) + 5(1 + 2Z) -135 + 64Z = (-1 * 2 + 4Z * 2) + 5(1 + 2Z) -135 + 64Z = (-2 + 8Z) + 5(1 + 2Z) -135 + 64Z = -2 + 8Z + (1 * 5 + 2Z * 5) -135 + 64Z = -2 + 8Z + (5 + 10Z) Reorder the terms: -135 + 64Z = -2 + 5 + 8Z + 10Z Combine like terms: -2 + 5 = 3 -135 + 64Z = 3 + 8Z + 10Z Combine like terms: 8Z + 10Z = 18Z -135 + 64Z = 3 + 18Z Solving -135 + 64Z = 3 + 18Z Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-18Z' to each side of the equation. -135 + 64Z + -18Z = 3 + 18Z + -18Z Combine like terms: 64Z + -18Z = 46Z -135 + 46Z = 3 + 18Z + -18Z Combine like terms: 18Z + -18Z = 0 -135 + 46Z = 3 + 0 -135 + 46Z = 3 Add '135' to each side of the equation. -135 + 135 + 46Z = 3 + 135 Combine like terms: -135 + 135 = 0 0 + 46Z = 3 + 135 46Z = 3 + 135 Combine like terms: 3 + 135 = 138 46Z = 138 Divide each side by '46'. Z = 3 Simplifying Z = 3
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