Solve 5(x-3)=2(x+1)-5(x-3)

$$5 ( x - 3 ) = 2 ( x + 1 ) - 5 ( x - 3 )$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

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

$$5x-15=2\left(x+1\right)-5\left(x-3\right)$$

Use the distributive property to multiply 2 by x+1.

$$5x-15=2x+2-5\left(x-3\right)$$

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

$$5x-15=2x+2-5x+15$$

Combine 2x and -5x to get -3x.

$$5x-15=-3x+2+15$$

Add 2 and 15 to get 17.

$$5x-15=-3x+17$$

Add 3x to both sides.

$$5x-15+3x=17$$

Combine 5x and 3x to get 8x.

$$8x-15=17$$

Add 15 to both sides.

$$8x=17+15$$

Add 17 and 15 to get 32.

$$8x=32$$

Divide both sides by 8.

$$x=\frac{32}{8}$$

Divide 32 by 8 to get 4.

$$x=4$$