Solve 6(-x+2)-(x-3)=3(-x+1)

$$6 ( - x + 2 ) - ( x - 3 ) = 3 ( - x + 1 )$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

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

$$6\left(-x\right)+12-\left(x-3\right)=3\left(-x+1\right)$$

To find the opposite of x-3, find the opposite of each term.

$$6\left(-x\right)+12-x-\left(-3\right)=3\left(-x+1\right)$$

The opposite of -3 is 3.

$$6\left(-x\right)+12-x+3=3\left(-x+1\right)$$

Add 12 and 3 to get 15.

$$6\left(-x\right)+15-x=3\left(-x+1\right)$$

Use the distributive property to multiply 3 by -x+1.

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

Subtract 3\left(-x\right) from both sides.

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

Combine 6\left(-x\right) and -3\left(-x\right) to get 3\left(-x\right).

$$3\left(-x\right)+15-x=3$$

Subtract 15 from both sides.

$$3\left(-x\right)-x=3-15$$

Subtract 15 from 3 to get -12.

$$3\left(-x\right)-x=-12$$

Multiply 3 and -1 to get -3.

$$-3x-x=-12$$

Combine -3x and -x to get -4x.

$$-4x=-12$$

Divide both sides by -4.

$$x=\frac{-12}{-4}$$

Divide -12 by -4 to get 3.

$$x=3$$