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

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

Solve for R

$$R=\frac{7x}{18}-\frac{5}{9}$$

Steps for Solving Linear Equation

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

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

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

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

Combine 3x and -x to get 2x.

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

Add -3 and 3 to get 0.

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

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

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

Combine 2x and 5x to get 7x.

$$7x-10=18R$$

Swap sides so that all variable terms are on the left hand side.

$$18R=7x-10$$

Divide both sides by 18.

$$\frac{18R}{18}=\frac{7x-10}{18}$$

Dividing by 18 undoes the multiplication by 18.

$$R=\frac{7x-10}{18}$$

Divide 7x-10 by 18.

$$R=\frac{7x}{18}-\frac{5}{9}$$

Solve for x

$$x=\frac{18R+10}{7}$$

Steps for Solving Linear Equation

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

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

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

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

Combine 3x and -x to get 2x.

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

Add -3 and 3 to get 0.

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

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

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

Combine 2x and 5x to get 7x.

$$7x-10=18R$$

Add 10 to both sides.

$$7x=18R+10$$

Divide both sides by 7.

$$\frac{7x}{7}=\frac{18R+10}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$x=\frac{18R+10}{7}$$