Question

solve for x.
\\(\dfrac{2x - 1}{x} + \dfrac{3x + 8}{5x} = 2\\)

Explanation:

Step1: Find LCM of denominators

Denominators are \(x\) and \(5x\), LCM is \(5x\). Multiply each term by \(5x\):
\(5x \cdot \frac{2x - 1}{x} + 5x \cdot \frac{3x + 8}{5x} = 5x \cdot 2\)

Step2: Simplify each term

Simplify: \(5(2x - 1) + (3x + 8) = 10x\)

Step3: Expand and combine like terms

Expand: \(10x - 5 + 3x + 8 = 10x\)
Combine: \(13x + 3 = 10x\)

Step4: Solve for \(x\)

Subtract \(13x\): \(3 = -3x\)
Divide: \(x = \frac{3}{-3} = -1\)

Answer:

\(x = -1\)