Solve for x: x - 2/3 = 2x/7
Solution:
In algebra, we use the balancing or the transposition method to solve for the unknown variable 'x'.
The value of 'x' can be calculated using two methods:
Balancing method:
x - 2/3 = 2x/7
Let's eliminate 2/3 from the left hand side of the equation by adding 2/3 on both sides of it:
x - 2/3 + 2/3 = 2x/7 + 2/3
or, x = 2x/7 + 2/3
Now subtract 2x/7 from both sides of the equation to make sure we have the terms with the variable on the left hand side of the equation.
x - 2x/7 = 2x/7 - 2x/7 + 2/3
or, x - 2x/7 = 2/3
or, 7x/7 - 2x/7 = 2/3
or, 5x/7 = 2/3
Multiplying both sides of the equation by 7/5, to have just the variable on the left-hand side of the equation:
5x/7 × 7/5 = 2/3 × 7/5
or, x = 14/15
Transposing method:
x - 2/3 = 2x/7
Transposing x to the right hand side of the equation, we get:
- 2/3 = 2x/7 - x
or, - 2/3 = 2x/7 - 7x/7
or, -2/3 = -5x/7
Multiplying both sides by -7/5, we get:
(-5x/7) × (-7/5) = (-2/3) × (-7/5)
or, x = 14/15
Therefore, the value of x is 14/15.
Solve for x: x - 2/3 = 2x/7
Summary:
The value of x for the given equation x - 2/3 = 2x/7 is 14/15.
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