Solve x-1/3-5x+2/8=2x-3/6+x-3/4

$$\frac { x - 1 } { 3 } - \frac { 5 x + 2 } { 8 } = \frac { 2 x - 3 } { 6 } + \frac { x - 3 } { 4 }$$

Solve for x

$$x=\frac{16}{21}\approx 0.761904762$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 3,8,6,4.

$$8\left(x-1\right)-3\left(5x+2\right)=4\left(2x-3\right)+6\left(x-3\right)$$

Use the distributive property to multiply 8 by x-1.

$$8x-8-3\left(5x+2\right)=4\left(2x-3\right)+6\left(x-3\right)$$

Use the distributive property to multiply -3 by 5x+2.

$$8x-8-15x-6=4\left(2x-3\right)+6\left(x-3\right)$$

Combine 8x and -15x to get -7x.

$$-7x-8-6=4\left(2x-3\right)+6\left(x-3\right)$$

Subtract 6 from -8 to get -14.

$$-7x-14=4\left(2x-3\right)+6\left(x-3\right)$$

Use the distributive property to multiply 4 by 2x-3.

$$-7x-14=8x-12+6\left(x-3\right)$$

Use the distributive property to multiply 6 by x-3.

$$-7x-14=8x-12+6x-18$$

Combine 8x and 6x to get 14x.

$$-7x-14=14x-12-18$$

Subtract 18 from -12 to get -30.

$$-7x-14=14x-30$$

Subtract 14x from both sides.

$$-7x-14-14x=-30$$

Combine -7x and -14x to get -21x.

$$-21x-14=-30$$

Add 14 to both sides.

$$-21x=-30+14$$

Add -30 and 14 to get -16.

$$-21x=-16$$

Divide both sides by -21.

$$x=\frac{-16}{-21}$$

Fraction \frac{-16}{-21} can be simplified to \frac{16}{21} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{16}{21}$$