Solve {l}{3x-7=3(5-x)}{3(2p-1)=5-(3p-2)}

$$\left. \begin{array} { l } { 3 x - 7 = 3 ( 5 - x ) } \\ { 3 ( 2 p - 1 ) = 5 - ( 3 p - 2 ) } \end{array} \right.$$

Solve for x, p

$$x = \frac{11}{3} = 3\frac{2}{3} \approx 3.666666667$$

$$p = \frac{10}{9} = 1\frac{1}{9} \approx 1.111111111$$

Solution Steps

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

$$3x-7=15-3x$$

Add 3x to both sides.

$$3x-7+3x=15$$

Combine 3x and 3x to get 6x.

$$6x-7=15$$

Add 7 to both sides.

$$6x=15+7$$

Add 15 and 7 to get 22.

$$6x=22$$

Divide both sides by 6.

$$x=\frac{22}{6}$$

Reduce the fraction \frac{22}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{11}{3}$$

Consider the second equation. Use the distributive property to multiply 3 by 2p-1.

$$6p-3=5-\left(3p-2\right)$$

To find the opposite of 3p-2, find the opposite of each term.

$$6p-3=5-3p+2$$

Add 5 and 2 to get 7.

$$6p-3=7-3p$$

Add 3p to both sides.

$$6p-3+3p=7$$

Combine 6p and 3p to get 9p.

$$9p-3=7$$

Add 3 to both sides.

$$9p=7+3$$

Add 7 and 3 to get 10.

$$9p=10$$

Divide both sides by 9.

$$p=\frac{10}{9}$$

The system is now solved.

$$x=\frac{11}{3} p=\frac{10}{9}$$