Question

(\frac{3x}{4} - \frac{x}{3} + 1 = \frac{4x}{5} - \frac{3}{20})

Explanation:

Step1: Eliminate denominators (LCM=60)

Multiply each term by 60:
$$60\times\frac{3x}{4} - 60\times\frac{x}{3} + 60\times1 = 60\times\frac{4x}{5} - 60\times\frac{3}{20}$$
Simplify each term:
$$45x - 20x + 60 = 48x - 9$$

Step2: Combine like terms on left

$$25x + 60 = 48x - 9$$

Step3: Isolate x terms to right

Subtract $25x$ from both sides:
$$60 = 23x - 9$$

Step4: Isolate constant terms to left

Add 9 to both sides:
$$69 = 23x$$

Step5: Solve for x

Divide both sides by 23:
$$x = \frac{69}{23}$$
$$x = 3$$

Answer:

$x=3$