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Solve the following linear equations for x: 1) 5x = 25 2) 12x − 36 = 0 3) 2x + 3 = 17. Also, simplify the expression -20 - 4x.

Mathematics

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Here are the solutions to the problems you sent:

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  1. Identify the equation.

    The equation is given as:

    5x=255x = 25
  2. Isolate xx by dividing both sides of the equation by 5.

    5x5=255\frac{5x}{5} = \frac{25}{5}
  3. Simplify both sides of the equation.

    x=5x = 5

    The solution is:

    x=5\boxed{x = 5}

    :
    The expression given is 12x−3612x - 36. This is an expression, not an equation, so it cannot be "solved" for xx without an equality. However, assuming it was intended to be an equation, for example, 12x−36=012x - 36 = 0, we can solve for xx.

    Assumption: The problem intended to be 12x−36=012x - 36 = 0.

  4. Identify the equation.

    12x−36=012x - 36 = 0
  5. Add 36 to both sides of the equation.

    12x−36+36=0+3612x - 36 + 36 = 0 + 36 12x=3612x = 36
  6. Divide both sides by 12 to isolate xx.

    12x12=3612\frac{12x}{12} = \frac{36}{12}
  7. Simplify both sides.

    x=3x = 3

    The solution (under the assumption 12x−36=012x - 36 = 0) is:

    x=3\boxed{x = 3}

    :

  8. Identify the equation.

    The equation is given as:

    2x+3=172x + 3 = 17
  9. Subtract 3 from both sides of the equation.

    2x+3−3=17−32x + 3 - 3 = 17 - 3 2x=142x = 14
  10. Divide both sides by 2 to isolate xx.

    2x2=142\frac{2x}{2} = \frac{14}{2}
  11. Simplify both sides.

    x=7x = 7

    The solution is:

    x=7\boxed{x = 7}

    :
    The expression given is −20−4x-20 - 4x. This is an expression, not an equation, so it cannot be "solved" for xx without an equality. However, assuming it was intended to be an equation, for example, −20−4x=0-20 - 4x = 0, we can solve for xx.

    Assumption: The problem intended to be −20−4x=0-20 - 4x = 0.

  12. Identify the equation.

    −20−4x=0-20 - 4x = 0
  13. Add 20 to both sides of the equation.

    −20−4x+20=0+20-20 - 4x + 20 = 0 + 20 −4x=20-4x = 20
  14. Divide both sides by -4 to isolate xx.

    −4x−4=20−4\frac{-4x}{-4} = \frac{20}{-4}
  15. Simplify both sides.

    x=−5x = -5

    The solution (under the assumption −20−4x=0-20 - 4x = 0) is:

    x=−5\boxed{x = -5}

    :

  16. Identify the equation.

    The equation is given as:

    22=2x22 = 2x
  17. Divide both sides by 2 to isolate xx.

    222=2x2\frac{22}{2} = \frac{2x}{2}
  18. Simplify both sides.

    11=x11 = x

    The solution is:

    x=11\boxed{x = 11}

    :

  19. Identify the equation.

    The equation is given as:

    c+5=5c + 5 = 5
  20. Subtract 5 from both sides of the equation.

    c+5−5=5−5c + 5 - 5 = 5 - 5
  21. Simplify both sides.

    c=0c = 0

    The solution is:

    c=0\boxed{c = 0}

    :

  22. Identify the equation.

    The equation is given as:

    b−11=12b - 11 = 12
  23. Add 11 to both sides of the equation.

    b−11+11=12+11b - 11 + 11 = 12 + 11
  24. Simplify both sides.

    b=23b = 23

    The solution is:

    b=23\boxed{b = 23}

    :

  25. Identify the equation.

    The equation is given as:

    c+1=7c + 1 = 7
  26. Subtract 1 from both sides of the equation.

    c+1−1=7−1c + 1 - 1 = 7 - 1
  27. Simplify both sides.

    c=6c = 6

    The solution is:

    c=6\boxed{c = 6}
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