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

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

Solve for x, y, z

$$z=2$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\times 3\left(x+1\right)+2\times 5\left(x+1\right)=24$$

Multiply 3 and 3 to get 9.

$$9\left(x+1\right)+2\times 5\left(x+1\right)=24$$

Use the distributive property to multiply 9 by x+1.

$$9x+9+2\times 5\left(x+1\right)=24$$

Multiply 2 and 5 to get 10.

$$9x+9+10\left(x+1\right)=24$$

Use the distributive property to multiply 10 by x+1.

$$9x+9+10x+10=24$$

Combine 9x and 10x to get 19x.

$$19x+9+10=24$$

Add 9 and 10 to get 19.

$$19x+19=24$$

Subtract 19 from both sides.

$$19x=24-19$$

Subtract 19 from 24 to get 5.

$$19x=5$$

Divide both sides by 19.

$$x=\frac{5}{19}$$

The system is now solved.

$$x=\frac{5}{19} y=2 z=2$$