Solve 1/53(x-1)-x+1/4=x+2-3(x-3)/2

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

Solve for x

$$x = \frac{147}{17} = 8\frac{11}{17} \approx 8.647058824$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 5,4,2.

$$4\times 3\left(x-1\right)-5\left(x+1\right)=20x+40-10\times 3\left(x-3\right)$$

Multiply 4 and 3 to get 12.

$$12\left(x-1\right)-5\left(x+1\right)=20x+40-10\times 3\left(x-3\right)$$

Use the distributive property to multiply 12 by x-1.

$$12x-12-5\left(x+1\right)=20x+40-10\times 3\left(x-3\right)$$

Use the distributive property to multiply -5 by x+1.

$$12x-12-5x-5=20x+40-10\times 3\left(x-3\right)$$

Combine 12x and -5x to get 7x.

$$7x-12-5=20x+40-10\times 3\left(x-3\right)$$

Subtract 5 from -12 to get -17.

$$7x-17=20x+40-10\times 3\left(x-3\right)$$

Multiply -10 and 3 to get -30.

$$7x-17=20x+40-30\left(x-3\right)$$

Use the distributive property to multiply -30 by x-3.

$$7x-17=20x+40-30x+90$$

Combine 20x and -30x to get -10x.

$$7x-17=-10x+40+90$$

Add 40 and 90 to get 130.

$$7x-17=-10x+130$$

Add 10x to both sides.

$$7x-17+10x=130$$

Combine 7x and 10x to get 17x.

$$17x-17=130$$

Add 17 to both sides.

$$17x=130+17$$

Add 130 and 17 to get 147.

$$17x=147$$

Divide both sides by 17.

$$x=\frac{147}{17}$$