Solve 3(x-1)-(x-3)+5(x-2)=18

$$3(x-1)-(x-3)+5(x-2)=18$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

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

$$3x-3-\left(x-3\right)+5\left(x-2\right)=18$$

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

$$3x-3-x-\left(-3\right)+5\left(x-2\right)=18$$

The opposite of -3 is 3.

$$3x-3-x+3+5\left(x-2\right)=18$$

Combine 3x and -x to get 2x.

$$2x-3+3+5\left(x-2\right)=18$$

Add -3 and 3 to get 0.

$$2x+5\left(x-2\right)=18$$

Use the distributive property to multiply 5 by x-2.

$$2x+5x-10=18$$

Combine 2x and 5x to get 7x.

$$7x-10=18$$

Add 10 to both sides.

$$7x=18+10$$

Add 18 and 10 to get 28.

$$7x=28$$

Divide both sides by 7.

$$x=\frac{28}{7}$$

Divide 28 by 7 to get 4.

$$x=4$$