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

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

Solve for x

$$x=-\frac{18}{23}\approx -0.782608696$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,2,4.

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

Use the distributive property to multiply 6 by x-5.

$$4x+6x-30-3x=6\left(5x-2\right)$$

Combine 4x and 6x to get 10x.

$$10x-30-3x=6\left(5x-2\right)$$

Combine 10x and -3x to get 7x.

$$7x-30=6\left(5x-2\right)$$

Use the distributive property to multiply 6 by 5x-2.

$$7x-30=30x-12$$

Subtract 30x from both sides.

$$7x-30-30x=-12$$

Combine 7x and -30x to get -23x.

$$-23x-30=-12$$

Add 30 to both sides.

$$-23x=-12+30$$

Add -12 and 30 to get 18.

$$-23x=18$$

Divide both sides by -23.

$$x=\frac{18}{-23}$$

Fraction \frac{18}{-23} can be rewritten as -\frac{18}{23} by extracting the negative sign.

$$x=-\frac{18}{23}$$