Solve {l}{frac{4{(x-1)}}{3}-2x-3/2=0}{y=5}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{4 {(x - 1)}}{3} - \frac{2 x - 3}{2} = 0 }\\ { y = 5 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=5$$

Solution Steps

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

$$2\times 4\left(x-1\right)-3\left(2x-3\right)=0$$

Multiply 2 and 4 to get 8.

$$8\left(x-1\right)-3\left(2x-3\right)=0$$

Use the distributive property to multiply 8 by x-1.

$$8x-8-3\left(2x-3\right)=0$$

Use the distributive property to multiply -3 by 2x-3.

$$8x-8-6x+9=0$$

Combine 8x and -6x to get 2x.

$$2x-8+9=0$$

Add -8 and 9 to get 1.

$$2x+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$2x=-1$$

Divide both sides by 2.

$$x=-\frac{1}{2}$$

The system is now solved.

$$x=-\frac{1}{2} y=5 z=5$$