(x+2)/5=(10-2x)/3 Thank You.

multiply each side by 15

3(x+2)=5(10-2x)
3x+6=50-10x
subtract six from each side, add 10x to each side
13x=44
x=44/13

what do you mean by multiply each side by 15. What is this method called?

it is called getting a common denominator, then eliminating it.

To solve the equation (x + 2)/5 = (10 - 2x)/3, we can follow these steps:

Step 1: Clear the denominators.
To do this, we multiply both sides of the equation by the least common multiple (LCM) of the denominators, which in this case is 15.

15 * [(x + 2)/5] = 15 * [(10 - 2x)/3]

This simplifies to:

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

Step 2: Distribute the terms.
Multiply both sides of the equation by the values inside the parentheses.

3x + 6 = 50 - 10x

Step 3: Combine like terms.
Combine the x terms and constants on both sides of the equation.

3x + 10x = 50 - 6

This simplifies to:

13x = 44

Step 4: Isolate x.
Divide both sides of the equation by the coefficient of x, which is 13.

x = 44/13

Step 5: Simplify the answer (if necessary).
If possible, simplify the resulting fraction. In this case, 44/13 is already in its simplest form.

Therefore, the solution to the equation (x + 2)/5 = (10 - 2x)/3 is x = 44/13.