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Solve the following equations using balancing method. 1. 2x = -10 2. 2y = 10 3. x/9 = -3 4. 8 = p/4 5. 8q − 16 = 0 6. z − 8 = 0 7. 2x/8 = 5 8. -8−5d = 7 9. m+10 = 16 10. -k+7 = 12

Mathematics

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Here are the solutions to the equations using the balancing method:

  1. 2x=−102x = -10
  1. Divide both sides by 2.

    $$
    \frac{2x}{2} = \frac{-10}{2}
    $$
    $$
    x = -5
    $$
    The solution is $\boxed{x = -5}$.
    

    2. 2y=102y = 10

  2. Divide both sides by 2.

    $$
    \frac{2y}{2} = \frac{10}{2}
    $$
    $$
    y = 5
    $$
    The solution is $\boxed{y = 5}$.
    

    3. x9=−3\frac{x}{9} = -3

  3. Multiply both sides by 9.

    $$
    \frac{x}{9} \times 9 = -3 \times 9
    $$
    $$
    x = -27
    $$
    The solution is $\boxed{x = -27}$.
    

    4. 8=p48 = \frac{p}{4}

  4. Multiply both sides by 4.

    $$
    8 \times 4 = \frac{p}{4} \times 4
    $$
    $$
    32 = p
    $$
    The solution is $\boxed{p = 32}$.
    

    5. 8q−16=08q - 16 = 0

  5. Add 16 to both sides.

    $$
    8q - 16 + 16 = 0 + 16
    $$
    $$
    8q = 16
    $$
    
  6. Divide both sides by 8.

    $$
    \frac{8q}{8} = \frac{16}{8}
    $$
    $$
    q = 2
    $$
    The solution is $\boxed{q = 2}$.
    

    6. z−8=0z - 8 = 0

  7. Add 8 to both sides.

    $$
    z - 8 + 8 = 0 + 8
    $$
    $$
    z = 8
    $$
    The solution is $\boxed{z = 8}$.
    

    7. 2x8=5\frac{2x}{8} = 5

  8. Multiply both sides by 8.

    $$
    \frac{2x}{8} \times 8 = 5 \times 8
    $$
    $$
    2x = 40
    $$
    
  9. Divide both sides by 2.

    $$
    \frac{2x}{2} = \frac{40}{2}
    $$
    $$
    x = 20
    $$
    The solution is $\boxed{x = 20}$.
    

    8. −8−5d=7-8 - 5d = 7

  10. Add 8 to both sides.

    $$
    -8 - 5d + 8 = 7 + 8
    $$
    $$
    -5d = 15
    $$
    
  11. Divide both sides by -5.

    $$
    \frac{-5d}{-5} = \frac{15}{-5}
    $$
    $$
    d = -3
    $$
    The solution is $\boxed{d = -3}$.
    

    9. m+10=16m + 10 = 16

  12. Subtract 10 from both sides.

    $$
    m + 10 - 10 = 16 - 10
    $$
    $$
    m = 6
    $$
    The solution is $\boxed{m = 6}$.
    

    10. −k+7=12-k + 7 = 12

  13. Subtract 7 from both sides.

    $$
    -k + 7 - 7 = 12 - 7
    $$
    $$
    -k = 5
    $$
    
  14. Multiply both sides by -1.

    $$
    -k \times (-1) = 5 \times (-1)
    $$
    $$
    k = -5
    $$
    The solution is $\boxed{k = -5}$.
    
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