Question

(\frac{x - 3}{5}-1=\frac{x - 5}{4})

Explanation:

Step1: Eliminate denominators (LCM=20)

Multiply each term by 20:
$$20\times\frac{x-3}{5} - 20\times1 = 20\times\frac{x-5}{4}$$
Simplify to get:
$$4(x-3) - 20 = 5(x-5)$$

Step2: Expand parentheses

Distribute coefficients:
$$4x - 12 - 20 = 5x - 25$$

Step3: Combine like terms

Simplify constants:
$$4x - 32 = 5x - 25$$

Step4: Isolate x terms

Subtract $4x$ from both sides:
$$-32 = x - 25$$

Step5: Solve for x

Add 25 to both sides:
$$x = -32 + 25$$

Answer:

$x = -7$