(2x-1)/5+4=(x+5)/2+1

2 min read Jun 16, 2024

Solving the Equation (2x-1)/5 + 4 = (x+5)/2 + 1

This article will guide you through the steps of solving the equation (2x-1)/5 + 4 = (x+5)/2 + 1.

1. Eliminate the fractions

To start, we need to eliminate the fractions. We can do this by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which is 10.

10 * [(2x-1)/5 + 4] = 10 * [(x+5)/2 + 1]

Simplifying this, we get:

2(2x-1) + 40 = 5(x+5) + 10

2. Expand and simplify

Next, we expand the brackets and simplify the equation.

4x - 2 + 40 = 5x + 25 + 10

4x + 38 = 5x + 35

3. Isolate the variable

To isolate the variable 'x', we need to move all the 'x' terms to one side and the constant terms to the other side.

38 - 35 = 5x - 4x

4. Solve for 'x'

Finally, we simplify the equation to find the value of 'x'.

3 = x

Therefore, the solution to the equation (2x-1)/5 + 4 = (x+5)/2 + 1 is x = 3.