Question

((x-1)/3) ((2x 1)/5)=((3x-1)/4)

Answer 1

The solutions for x in the equation
`\(\frac{{(x-1)}}{3} \cdot \frac{{(2x+1)}}{5} = \frac{{(3x-1)}}{4}\)` are x = 1 or
`\(x = (5)/(8)\)`.

Let's consider the given equation in its entirety:

`\[ \frac{{(x-1)}}{3} \cdot \frac{{(2x+1)}}{5} = \frac{{(3x-1)}}{4} \]`

To solve this equation, follow these steps:

1. Clear Fractions:

Multiply both sides by the least common denominator, which is 60 (the product of 3, 5, and 4):

`\[ 60 \cdot \frac{{(x-1)}}{3} \cdot \frac{{(2x+1)}}{5} = 60 \cdot \frac{{(3x-1)}}{4} \]`

This simplifies to:

`\[ 20(x-1)(2x+1) = 15(3x-1) \]`

2. Expand:

Expand both sides of the equation:

`\[ 40x^2 - 20x - 40 = 45x - 15 \]`

3. Collect Terms:

Move all terms to one side of the equation:

`\[ 40x^2 - 65x + 25 = 0 \]`

4. Factor or Use Quadratic Formula:

To find the values of x in the equation
`\(40x^2 - 65x + 25 = 0\)`, we can use the quadratic formula:

`\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \]`

`\[ x = \frac{{65 \pm \sqrt{{4225 - 4000}}}}{80} \]`

`\[ x = \frac{{65 \pm \sqrt{{225}}}}{80} \]`

`\[ x = \frac{{65 \pm 15}}{80} \]`

So, the solutions for x are:

`\[ x = (8)/(8) \quad \text{or} \quad x = (5)/(8) \]`

Therefore, x can be either 1 or
`\((5)/(8)\)`.

Que. ((x-1)/3) ((2x 1)/5)=((3x-1)/4) Find x?