Solve {l}{p=6.3}{q=-8.7}{r=-9.9}{s=r+p+|p|+q}{t=s}{u=t}{v=u}{w=v}{text{Solvefor}xtext{where}}{x=w}

$$\left. \begin{array} { l } { p = 6.3 }\\ { q = -8.7 }\\ { r = -9.9 }\\ { s = r + p + | p | + q }\\ { t = s }\\ { u = t }\\ { v = u }\\ { w = v }\\ { \text{Solve for } x \text{ where} } \\ { x = w } \end{array} \right.$$

Solve for p, q, r, s, t, u, v, w, x

$$x=-6$$

Solution Steps

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

$$s=-9.9+6.3+|6.3|-8.7$$

Add -9.9 and 6.3 to get -3.6.

$$s=-3.6+|6.3|-8.7$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 6.3 is 6.3.

$$s=-3.6+6.3-8.7$$

Add -3.6 and 6.3 to get 2.7.

$$s=2.7-8.7$$

Subtract 8.7 from 2.7 to get -6.

$$s=-6$$

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

$$t=-6$$

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

$$u=-6$$

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

$$v=-6$$

Consider the equation (8). Insert the known values of variables into the equation.

$$w=-6$$

Consider the equation (9). Insert the known values of variables into the equation.

$$x=-6$$

The system is now solved.

$$p=6.3 q=-8.7 r=-9.9 s=-6 t=-6 u=-6 v=-6 w=-6 x=-6$$