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Simplify the following algebraic expressions:

Mathematics

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Step-by-step solution

18 steps

Here are the simplified algebraic expressions:

  1. 16x+9x−616x + 9x - 6
  1. Combine the terms with xx.

    $$
    (16+9)x - 6 = 25x - 6
    $$
    The simplified expression is $\boxed{25x - 6}$.
    

    2. 2+5d+6+9d2 + 5d + 6 + 9d

  2. Group like terms.

    $$
    (5d + 9d) + (2 + 6)
    $$
    
  3. Combine like terms.

    $$
    (5+9)d + (2+6) = 14d + 8
    $$
    The simplified expression is $\boxed{14d + 8}$.
    

    3. −8c+2−4+5c-8c + 2 - 4 + 5c

  4. Group like terms.

    $$
    (-8c + 5c) + (2 - 4)
    $$
    
  5. Combine like terms.

    $$
    (-8+5)c + (2-4) = -3c - 2
    $$
    The simplified expression is $\boxed{-3c - 2}$.
    

    4. 5m−9m−25m - 9m - 2

  6. Combine the terms with mm.

    $$
    (5-9)m - 2 = -4m - 2
    $$
    The simplified expression is $\boxed{-4m - 2}$.
    

    5. 8+7g−58 + 7g - 5

  7. Group like terms.

    $$
    7g + (8 - 5)
    $$
    
  8. Combine like terms.

    $$
    7g + 3
    $$
    The simplified expression is $\boxed{7g + 3}$.
    

    6. 10y−9−15+8y10y - 9 - 15 + 8y

  9. Group like terms.

    $$
    (10y + 8y) + (-9 - 15)
    $$
    
  10. Combine like terms.

    $$
    (10+8)y + (-9-15) = 18y - 24
    $$
    The simplified expression is $\boxed{18y - 24}$.
    

    7. 13+18w−1413 + 18w - 14

  11. Group like terms.

    $$
    18w + (13 - 14)
    $$
    
  12. Combine like terms.

    $$
    18w - 1
    $$
    The simplified expression is $\boxed{18w - 1}$.
    

    8. 3−19+9b−17b3 - 19 + 9b - 17b

  13. Group like terms.

    $$
    (9b - 17b) + (3 - 19)
    $$
    
  14. Combine like terms.

    $$
    (9-17)b + (3-19) = -8b - 16
    $$
    The simplified expression is $\boxed{-8b - 16}$.
    

    9. −4+2x+9x+10-4 + 2x + 9x + 10

  15. Group like terms.

    $$
    (2x + 9x) + (-4 + 10)
    $$
    
  16. Combine like terms.

    $$
    (2+9)x + (-4+10) = 11x + 6
    $$
    The simplified expression is $\boxed{11x + 6}$.
    

    10. 11z−15+19z11z - 15 + 19z

  17. Group like terms.

    $$
    (11z + 19z) - 15
    $$
    
  18. Combine like terms.

    $$
    (11+19)z - 15 = 30z - 15
    $$
    The simplified expression is $\boxed{30z - 15}$.
    
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