Find x in (2x + 5)/3= 3x - 10.

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

Answer: The value of x in the given equation (2x + 5)/3= 3x - 10  is 5.

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:

(2x + 5)/3= 3x - 10

Let's multiply 3 on both sides of the equation to remove the fraction from the left hand side:

{(2x + 5)/3} × 3 = (3x - 10) × 3

or, 2x + 5 = 9x - 30

Let's now subtract 5 from both sides of the equation to have only the variable term on the left-hand side of the equation:

2x + 5 - 5 = 9x - 30 - 5

or, 2x = 9x - 35

Let's now subtract 9x from both sides of the equation to have the terms with the variable on the left-hand side of the equation:

or, 2x - 9x = 9x - 9x - 35

or, -7x = -35

Dividing both sides of the equation by -7 to find the value of the variable x, we get:

-7x/(-7) = -35/(-7)

or, x = 5

• Transposing method:

(2x + 5)/3= 3x - 10

Transposing 3 to the right hand side of the equation, we get:

2x + 5 = (3x - 10) × 3

or, 2x + 5 = 9x - 30

Transposing 9x to the left-hand side of the equation in order to keep the terms with the variable on one side of the equation, we get:

or, 2x - 9x + 5 =  - 30

Transposing 5 to the right hand side of the equation, we get:

or, 2x - 9x =  - 30 - 5

or, -7x = -35

Dividing both sides by -7, we get:

-7x/(-7) = -35/(-7)

or, x = 5

Therefore, the value of x in the given equation (2x + 5)/3= 3x - 10 is 5.