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Simplifying -11(-20z + -7) + -16(12z + -2) = -17(8z + 5) + 2 + -10z Reorder the terms: -11(-7 + -20z) + -16(12z + -2) = -17(8z + 5) + 2 + -10z (-7 * -11 + -20z * -11) + -16(12z + -2) = -17(8z + 5) + 2 + -10z (77 + 220z) + -16(12z + -2) = -17(8z + 5) + 2 + -10z Reorder the terms: 77 + 220z + -16(-2 + 12z) = -17(8z + 5) + 2 + -10z 77 + 220z + (-2 * -16 + 12z * -16) = -17(8z + 5) + 2 + -10z 77 + 220z + (32 + -192z) = -17(8z + 5) + 2 + -10z Reorder the terms: 77 + 32 + 220z + -192z = -17(8z + 5) + 2 + -10z Combine like terms: 77 + 32 = 109 109 + 220z + -192z = -17(8z + 5) + 2 + -10z Combine like terms: 220z + -192z = 28z 109 + 28z = -17(8z + 5) + 2 + -10z Reorder the terms: 109 + 28z = -17(5 + 8z) + 2 + -10z 109 + 28z = (5 * -17 + 8z * -17) + 2 + -10z 109 + 28z = (-85 + -136z) + 2 + -10z Reorder the terms: 109 + 28z = -85 + 2 + -136z + -10z Combine like terms: -85 + 2 = -83 109 + 28z = -83 + -136z + -10z Combine like terms: -136z + -10z = -146z 109 + 28z = -83 + -146z Solving 109 + 28z = -83 + -146z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '146z' to each side of the equation. 109 + 28z + 146z = -83 + -146z + 146z Combine like terms: 28z + 146z = 174z 109 + 174z = -83 + -146z + 146z Combine like terms: -146z + 146z = 0 109 + 174z = -83 + 0 109 + 174z = -83 Add '-109' to each side of the equation. 109 + -109 + 174z = -83 + -109 Combine like terms: 109 + -109 = 0 0 + 174z = -83 + -109 174z = -83 + -109 Combine like terms: -83 + -109 = -192 174z = -192 Divide each side by '174'. z = -1.103448276 Simplifying z = -1.103448276
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