Solve 3x+5/2-4x-5/3=7x+1/

$$\frac{ 3x+5 }{ 2 } - \frac{ 4x-5 }{ 3 } = \frac{ 7x+1 }{ }$$

Solve for x

$$x=\frac{19}{41}\approx 0.463414634$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(3x+5\right)-2\left(4x-5\right)=6\left(7x+1\right)$$

Use the distributive property to multiply 3 by 3x+5.

$$9x+15-2\left(4x-5\right)=6\left(7x+1\right)$$

Use the distributive property to multiply -2 by 4x-5.

$$9x+15-8x+10=6\left(7x+1\right)$$

Combine 9x and -8x to get x.

$$x+15+10=6\left(7x+1\right)$$

Add 15 and 10 to get 25.

$$x+25=6\left(7x+1\right)$$

Use the distributive property to multiply 6 by 7x+1.

$$x+25=42x+6$$

Subtract 42x from both sides.

$$x+25-42x=6$$

Combine x and -42x to get -41x.

$$-41x+25=6$$

Subtract 25 from both sides.

$$-41x=6-25$$

Subtract 25 from 6 to get -19.

$$-41x=-19$$

Divide both sides by -41.

$$x=\frac{-19}{-41}$$

Fraction \frac{-19}{-41} can be simplified to \frac{19}{41} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{19}{41}$$