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Solve the following algebraic equations:

Mathematics

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Step-by-step solution

11 steps

Here are the solutions to the algebraic equations:

  1. x+6=9x+6=9
  1. Subtract 6 from both sides of the equation.

    $$
    x = 9 - 6
    $$
    $$
    x = \boxed{\text{3}}
    $$
    

    2. x−6=9x-6=9

  2. Add 6 to both sides of the equation.

    $$
    x = 9 + 6
    $$
    $$
    x = \boxed{\text{15}}
    $$
    

    3. y+7=4y+7=4

  3. Subtract 7 from both sides of the equation.

    $$
    y = 4 - 7
    $$
    $$
    y = \boxed{\text{-3}}
    $$
    

    4. y−7=4y-7=4

  4. Add 7 to both sides of the equation.

    $$
    y = 4 + 7
    $$
    $$
    y = \boxed{\text{11}}
    $$
    

    5. n+2=−5n+2=-5

  5. Subtract 2 from both sides of the equation.

    $$
    n = -5 - 2
    $$
    $$
    n = \boxed{\text{-7}}
    $$
    

    6. n−2=−5n-2=-5

  6. Add 2 to both sides of the equation.

    $$
    n = -5 + 2
    $$
    $$
    n = \boxed{\text{-3}}
    $$
    

    7. x+3=0x+3=0

  7. Subtract 3 from both sides of the equation.

    $$
    x = 0 - 3
    $$
    $$
    x = \boxed{\text{-3}}
    $$
    

    8. x−3=0x-3=0

  8. Add 3 to both sides of the equation.

    $$
    x = 0 + 3
    $$
    $$
    x = \boxed{\text{3}}
    $$
    

    9. y+6=−8y+6=-8

  9. Subtract 6 from both sides of the equation.

    $$
    y = -8 - 6
    $$
    $$
    y = \boxed{\text{-14}}
    $$
    

    10. −x−4=−1-x-4=-1

  10. Add 4 to both sides of the equation.

    $$
    -x = -1 + 4
    $$
    $$
    -x = 3
    $$
    
  11. Multiply both sides by -1.

    $$
    x = \boxed{\text{-3}}
    $$
    
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