Solve 2x/3-2x+1/6=3x-5/4

$$\frac { 2 x } { 3 } - \frac { 2 x + 1 } { 6 } = \frac { 3 x - 5 } { 4 }$$

Solve for x

$$x = \frac{13}{5} = 2\frac{3}{5} = 2.6$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,6,4.

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

Multiply 4 and 2 to get 8.

$$8x-2\left(2x+1\right)=3\left(3x-5\right)$$

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

$$8x-4x-2=3\left(3x-5\right)$$

Combine 8x and -4x to get 4x.

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

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.

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

Add 2 to both sides.

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

Add -15 and 2 to get -13.

$$-5x=-13$$

Divide both sides by -5.

$$x=\frac{-13}{-5}$$

Fraction \frac{-13}{-5} can be simplified to \frac{13}{5} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{13}{5}$$