Solve {l}{7.5{(x+8.3)}=-4.5{(x+8.9)}+199.5}{y=x}{z=y}{a=z}{b=a}{c=b}{text{Solvefor}dtext{where}}{d=c}

$$\left. \begin{array} { l } { 7.5 {(x + 8.3)} = -4.5 {(x + 8.9)} + 199.5 }\\ { y = x }\\ { z = y }\\ { a = z }\\ { b = a }\\ { c = b }\\ { \text{Solve for } d \text{ where} } \\ { d = c } \end{array} \right.$$

Solve for x, y, z, a, b, c, d

$$d=8.1$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 7.5 by x+8.3.

$$7.5x+62.25=-4.5\left(x+8.9\right)+199.5$$

Use the distributive property to multiply -4.5 by x+8.9.

$$7.5x+62.25=-4.5x-40.05+199.5$$

Add -40.05 and 199.5 to get 159.45.

$$7.5x+62.25=-4.5x+159.45$$

Add 4.5x to both sides.

$$7.5x+62.25+4.5x=159.45$$

Combine 7.5x and 4.5x to get 12x.

$$12x+62.25=159.45$$

Subtract 62.25 from both sides.

$$12x=159.45-62.25$$

Subtract 62.25 from 159.45 to get 97.2.

$$12x=97.2$$

Divide both sides by 12.

$$x=\frac{97.2}{12}$$

Expand \frac{97.2}{12} by multiplying both numerator and the denominator by 10.

$$x=\frac{972}{120}$$

Reduce the fraction \frac{972}{120} to lowest terms by extracting and canceling out 12.

$$x=\frac{81}{10}$$

Consider the second equation. Insert the known values of variables into the equation.

$$y=\frac{81}{10}$$

Consider the third equation. Insert the known values of variables into the equation.

$$z=\frac{81}{10}$$

Consider the fourth equation. Insert the known values of variables into the equation.

$$a=\frac{81}{10}$$

Consider the fifth equation. Insert the known values of variables into the equation.

$$b=\frac{81}{10}$$

Consider the equation (6). Insert the known values of variables into the equation.

$$c=\frac{81}{10}$$

Consider the equation (7). Insert the known values of variables into the equation.

$$d=\frac{81}{10}$$

The system is now solved.

$$x=\frac{81}{10} y=\frac{81}{10} z=\frac{81}{10} a=\frac{81}{10} b=\frac{81}{10} c=\frac{81}{10} d=\frac{81}{10}$$