Solve 2(x-1)/3-2x+2/2=x-10

$$\frac { 2 ( x - 1 ) } { 3 } - \frac { 2 x + 2 } { 2 } = x - 10$$

Solve for x

$$x = \frac{25}{4} = 6\frac{1}{4} = 6.25$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2\times 2\left(x-1\right)-3\left(2x+2\right)=6x-60$$

Multiply 2 and 2 to get 4.

$$4\left(x-1\right)-3\left(2x+2\right)=6x-60$$

Use the distributive property to multiply 4 by x-1.

$$4x-4-3\left(2x+2\right)=6x-60$$

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

$$4x-4-6x-6=6x-60$$

Combine 4x and -6x to get -2x.

$$-2x-4-6=6x-60$$

Subtract 6 from -4 to get -10.

$$-2x-10=6x-60$$

Subtract 6x from both sides.

$$-2x-10-6x=-60$$

Combine -2x and -6x to get -8x.

$$-8x-10=-60$$

Add 10 to both sides.

$$-8x=-60+10$$

Add -60 and 10 to get -50.

$$-8x=-50$$

Divide both sides by -8.

$$x=\frac{-50}{-8}$$

Reduce the fraction \frac{-50}{-8} to lowest terms by extracting and canceling out -2.

$$x=\frac{25}{4}$$