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

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

Solve for x

$$x = \frac{97}{29} = 3\frac{10}{29} \approx 3.344827586$$

Steps for Solving Linear Equation

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

$$3\left(x+3\right)+2\left(2x-1\right)=18\left(2x-5\right)$$

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

$$3x+9+2\left(2x-1\right)=18\left(2x-5\right)$$

Use the distributive property to multiply 2 by 2x-1.

$$3x+9+4x-2=18\left(2x-5\right)$$

Combine 3x and 4x to get 7x.

$$7x+9-2=18\left(2x-5\right)$$

Subtract 2 from 9 to get 7.

$$7x+7=18\left(2x-5\right)$$

Use the distributive property to multiply 18 by 2x-5.

$$7x+7=36x-90$$

Subtract 36x from both sides.

$$7x+7-36x=-90$$

Combine 7x and -36x to get -29x.

$$-29x+7=-90$$

Subtract 7 from both sides.

$$-29x=-90-7$$

Subtract 7 from -90 to get -97.

$$-29x=-97$$

Divide both sides by -29.

$$x=\frac{-97}{-29}$$

Fraction \frac{-97}{-29} can be simplified to \frac{97}{29} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{97}{29}$$