# Solve for x: x - 2/3 = 2x/7

In algebra, we use the balancing or the transposition method to solve for the unknown variable 'x'.

## Answer: The value of x for the given equation x - 2/3 = 2x/7 is 14/15.

Let's now find the required value of x from the given equation.

**Explanation:**

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