Solve (3x+2)/(5x-1)=13/10

$$\frac { ( 3 x + 2 ) } { ( 5 x - 1 ) } = \frac { 13 } { 10 }$$

Solve for x

$$x=\frac{33}{35}\approx 0.942857143$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{1}{5} since division by zero is not defined. Multiply both sides of the equation by 10\left(5x-1\right), the least common multiple of 5x-1,10.

$$10\left(3x+2\right)=13\left(5x-1\right)$$

Use the distributive property to multiply 10 by 3x+2.

$$30x+20=13\left(5x-1\right)$$

Use the distributive property to multiply 13 by 5x-1.

$$30x+20=65x-13$$

Subtract 65x from both sides.

$$30x+20-65x=-13$$

Combine 30x and -65x to get -35x.

$$-35x+20=-13$$

Subtract 20 from both sides.

$$-35x=-13-20$$

Subtract 20 from -13 to get -33.

$$-35x=-33$$

Divide both sides by -35.

$$x=\frac{-33}{-35}$$

Fraction \frac{-33}{-35} can be simplified to \frac{33}{35} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{33}{35}$$