1) 4 - 2x/3 + x/6 = 0 To solve this equation, we first need to find a common denominator for the fractions. The common denominator in this case is 6. Multiplying the entire equation by 6, we get: 24 - 4x + x = 0 Combining like terms, we get: 24 - 3x = 0 Rearranging the equation, we get: 3x = 24 x = 8
Therefore, the solution to the equation 4 - 2x/3 + x/6 = 0 is x = 8.
2) x/6 - 2 = x/4 + 1 To solve this equation, we first need to find a common denominator for the fractions. The common denominator in this case is 12. Multiplying the entire equation by 12, we get: 2x - 24 = 3x + 12 Rearranging the equation, we get: 2x - 3x = 24 + 12 -x = 36 x = -36
Therefore, the solution to the equation x/6 - 2 = x/4 + 1 is x = -36.
3) x/4 + 2 = x/10 - 1 To solve this equation, we first need to find a common denominator for the fractions. The common denominator in this case is 20. Multiplying the entire equation by 20, we get: 5x + 40 = 2x - 20 Rearranging the equation, we get: 5x - 2x = -20 - 40 3x = -60 x = -20
Therefore, the solution to the equation x/4 + 2 = x/10 - 1 is x = -20.
I will solve each of these equations one by one:
1) 4 - 2x/3 + x/6 = 0
To solve this equation, we first need to find a common denominator for the fractions. The common denominator in this case is 6.
Multiplying the entire equation by 6, we get:
24 - 4x + x = 0
Combining like terms, we get:
24 - 3x = 0
Rearranging the equation, we get:
3x = 24
x = 8
Therefore, the solution to the equation 4 - 2x/3 + x/6 = 0 is x = 8.
2) x/6 - 2 = x/4 + 1
To solve this equation, we first need to find a common denominator for the fractions. The common denominator in this case is 12.
Multiplying the entire equation by 12, we get:
2x - 24 = 3x + 12
Rearranging the equation, we get:
2x - 3x = 24 + 12
-x = 36
x = -36
Therefore, the solution to the equation x/6 - 2 = x/4 + 1 is x = -36.
3) x/4 + 2 = x/10 - 1
To solve this equation, we first need to find a common denominator for the fractions. The common denominator in this case is 20.
Multiplying the entire equation by 20, we get:
5x + 40 = 2x - 20
Rearranging the equation, we get:
5x - 2x = -20 - 40
3x = -60
x = -20
Therefore, the solution to the equation x/4 + 2 = x/10 - 1 is x = -20.