Solve 3x-2/2+3(2x-1)=x+4/7-(x-1)

$$\frac { 3 x - 2 } { 2 } + 3 ( 2 x - 1 ) = \frac { x + 4 } { 7 } - ( x - 1 )$$

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 14, the least common multiple of 2,7.

$$7\left(3x-2\right)+42\left(2x-1\right)=2\left(x+4\right)-14\left(x-1\right)$$

Use the distributive property to multiply 7 by 3x-2.

$$21x-14+42\left(2x-1\right)=2\left(x+4\right)-14\left(x-1\right)$$

Use the distributive property to multiply 42 by 2x-1.

$$21x-14+84x-42=2\left(x+4\right)-14\left(x-1\right)$$

Combine 21x and 84x to get 105x.

$$105x-14-42=2\left(x+4\right)-14\left(x-1\right)$$

Subtract 42 from -14 to get -56.

$$105x-56=2\left(x+4\right)-14\left(x-1\right)$$

Use the distributive property to multiply 2 by x+4.

$$105x-56=2x+8-14\left(x-1\right)$$

Use the distributive property to multiply -14 by x-1.

$$105x-56=2x+8-14x+14$$

Combine 2x and -14x to get -12x.

$$105x-56=-12x+8+14$$

Add 8 and 14 to get 22.

$$105x-56=-12x+22$$

Add 12x to both sides.

$$105x-56+12x=22$$

Combine 105x and 12x to get 117x.

$$117x-56=22$$

Add 56 to both sides.

$$117x=22+56$$

Add 22 and 56 to get 78.

$$117x=78$$

Divide both sides by 117.

$$x=\frac{78}{117}$$

Reduce the fraction \frac{78}{117} to lowest terms by extracting and canceling out 39.

$$x=\frac{2}{3}$$