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

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

Solve for x

$$x = \frac{17}{5} = 3\frac{2}{5} = 3.4$$

Steps for Solving Linear Equation

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

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

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

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

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

$$4x+2=9x-15$$

Subtract 9x from both sides.

$$4x+2-9x=-15$$

Combine 4x and -9x to get -5x.

$$-5x+2=-15$$

Subtract 2 from both sides.

$$-5x=-15-2$$

Subtract 2 from -15 to get -17.

$$-5x=-17$$

Divide both sides by -5.

$$x=\frac{-17}{-5}$$

Fraction \frac{-17}{-5} can be simplified to \frac{17}{5} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{17}{5}$$