Solve {l}{x+3/4-x-3/5=2x}{y=5}{text{Solvefor}ztext{where}}{z=y}

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

Solve for x, y, z

$$z=5$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 20, the least common multiple of 4,5.

$$5\left(x+3\right)-4\left(x-3\right)=40x$$

Use the distributive property to multiply 5 by x+3.

$$5x+15-4\left(x-3\right)=40x$$

Use the distributive property to multiply -4 by x-3.

$$5x+15-4x+12=40x$$

Combine 5x and -4x to get x.

$$x+15+12=40x$$

Add 15 and 12 to get 27.

$$x+27=40x$$

Subtract 40x from both sides.

$$x+27-40x=0$$

Combine x and -40x to get -39x.

$$-39x+27=0$$

Subtract 27 from both sides. Anything subtracted from zero gives its negation.

$$-39x=-27$$

Divide both sides by -39.

$$x=\frac{-27}{-39}$$

Reduce the fraction \frac{-27}{-39} to lowest terms by extracting and canceling out -3.

$$x=\frac{9}{13}$$

The system is now solved.

$$x=\frac{9}{13} y=5 z=5$$