Solve {l}{x+1/5+x-2/3=4}{y={(67/8)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{x + 1}{5} + \frac{x - 2}{3} = 4 }\\ { y = {(\frac{67}{8})} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{67}{8} = 8\frac{3}{8} = 8.375$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$3\left(x+1\right)+5\left(x-2\right)=60$$

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

$$3x+3+5\left(x-2\right)=60$$

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

$$3x+3+5x-10=60$$

Combine 3x and 5x to get 8x.

$$8x+3-10=60$$

Subtract 10 from 3 to get -7.

$$8x-7=60$$

Add 7 to both sides.

$$8x=60+7$$

Add 60 and 7 to get 67.

$$8x=67$$

Divide both sides by 8.

$$x=\frac{67}{8}$$

The system is now solved.

$$x=\frac{67}{8} y=\frac{67}{8} z=\frac{67}{8}$$