Solve {l}{5p+4=18-{(2-p)}}{q=p}{text{Solvefor}rtext{where}}{r=q}

$$\left. \begin{array} { l } { 5 p + 4 = 18 - {(2 - p)} }\\ { q = p }\\ { \text{Solve for } r \text{ where} } \\ { r = q } \end{array} \right.$$

Solve for p, q, r

$$r=3$$

Solution Steps

Consider the first equation. To find the opposite of 2-p, find the opposite of each term.

$$5p+4=18-2+p$$

Subtract 2 from 18 to get 16.

$$5p+4=16+p$$

Subtract p from both sides.

$$5p+4-p=16$$

Combine 5p and -p to get 4p.

$$4p+4=16$$

Subtract 4 from both sides.

$$4p=16-4$$

Subtract 4 from 16 to get 12.

$$4p=12$$

Divide both sides by 4.

$$p=\frac{12}{4}$$

Divide 12 by 4 to get 3.

$$p=3$$

Consider the second equation. Insert the known values of variables into the equation.

$$q=3$$

Consider the third equation. Insert the known values of variables into the equation.

$$r=3$$

The system is now solved.

$$p=3 q=3 r=3$$