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

2 min read Jun 16, 2024

Solving the Equation (x+2)/5 = (10-2x)/3

This article will guide you through the steps of solving the equation (x+2)/5 = (10-2x)/3. We will use the principles of algebraic manipulation to isolate x and find its value.

1. Eliminate Fractions

To get rid of the fractions, we multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 15.

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

This simplifies to:

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

2. Expand the Equation

Now, we distribute the constants on both sides of the equation:

3x + 6 = 50 - 10x

3. Combine Like Terms

Move all x terms to one side and all constant terms to the other side:

3x + 10x = 50 - 6
13x = 44

4. Isolate x

Finally, divide both sides by 13 to isolate x:

x = 44/13

Solution

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